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Exploiting Tanzania

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So a massive helium reserve may have been found in Tanzania's Rift Valley. Wonderful. All the western headlines this morning have put a typically western spin on it. Hurrah! We are saved! We get to go plunder a foreign place again for what we need to save our own lives! Before we get too carried away with ourselves, let's take a few seconds to think about a few things. Like, say, how many MRI scanners are there in Tanzania right now? How many Tanzanian lives will be saved? Anyone care to estimate? This scanner in Dar es Salaam makes headlines when it breaks down.



What about the wildlife in Tanzania? Will lives be saved there, too? Note the concentration of national parks and game reserves in and around the Rukwa region of Tanzania. Now, I'm not intimately familiar with how helium gas is extracted, concentrated or liquefied but I'm going to guess that some of it has to be done where the gas is found. Even if the gas doesn't just float conveniently into collection chambers instead of needing some sort of gas forcing process (We love fracking, right?) and miles and miles of pipelines, it's a fair assumption that there will be massive energy needs to liquefy it. Then the cryogenic liquid helium must be transported. So we'll need roads, maybe an airport for the suits to get in and out quickly, and perhaps a railway to move the product to a sea port. Or we could just push the gas down a long pipe to the coast where it could be liquefied, then transported abroad. This is all going to be great news for African nature, I'm sure of it!


I would prefer that we take our cue from the researchers quoted in the BBC article.

Prof Chris Ballentine, of the Department of Earth Sciences at the University of Oxford, said: "This is a game-changer for the future security of society's helium needs and similar finds in the future may not be far away."

And colleague Dr Pete Barry added: "We can apply this same strategy to other parts of the world with a similar geological history to find new helium resources."

Good, because taking the usual westerners'"easy out" and exploiting the far away place where nimbys don't exist (and can be ignored even if they do) is the coward's solution. Let's go find helium in the Cascades or Hawaii or somewhere closer to those who actually get to benefit from MRI, then see how we react to the extraction options.

In the mean time, here's what Rukwa, Tanzania looks like today. This is the Katavi National Park, right in the middle of the Rukwa region.



Here's what the National Helium Reserve in Amarillo, Texas looks like.



Practically twins! And finally, here's what the Rukwa mine project looks like. This is the coal mine where the coal for producing electricity in the local power plant comes from. Because we'll be needing electricity. Lots of it. Global warming shmobal warming.



 Hurrah! We are saved! MRI for westerners forever!

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Update on 30 June, 2016:

I found the location of the helium reserve on the Helium One website. I estimated the location of the Rukwa Project, as it's called, on a Google map below. Many media outlets reported the helium find as being a "game changer." Freudian slip? Perhaps a game reserve changer at a minimum.



And for the record, as I hope I made clear in response to the comments from sfz, I'm not yet either for or against developing this gas field. I am against incomplete journalism, however. There are many issues that need to be addressed and questions asked from the developed countries who stand to benefit the most from this discovery.

Update on 1st July, 2016:

Looks like a new airport won't be needed. A new airport in nearby Mbeya opened in 2012 with an 11,000 ft runway. Now if we can only learn about the ways drilling might proceed with minimal impact on the game reserve. There's more science in a brief article online by Jon Gluyas, a member of of the team that developed the search methods and found the Rukwa reserve.





Starting points for SMS-EPI at 3 T: Part II

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In an earlier post I presented three starting protocols for the CMRR version of SMS-EPI, referred to as the MB-EPI sequence here. I'll use italics to indicate a specific pulse sequence whereas SMS-EPI, no italics, refers to the family of simultaneous multi-slice methods. In this post I'll develop a similar set of three starting protocols for the Massachusetts General Hospital (MGH) version of SMS-EPI, called Blipped-CAIPI. I'm going to build upon the explanations of the last post so please cross reference for parameter explanations and background.

As for the previous post there are several things to bear in mind. This series is Siemens-centric, specifically Trio-centric. While many of the concepts and parameter options may apply to other platforms there will be minor differences in parameter naming conventions and, perhaps, major differences in implementation that you will need to consider before you proceed. For Siemens users, I am running aging software, syngoMR version B17A. The age of the software and the old reconstruction board on the scanner means that you can expect to see much faster reconstruction on a newer system. I hope, but cannot guarantee, that the actual image quality and artifact level won't differ massively from a Trio running VB17A to a new Prisma running VE11C. I'll keep you updated as I learn more.


Preliminaries

As before, for this post I am going to be using a 32-channel receive-only head coil. The SMS-EPI sequences can be made to work with a 12-channel coil but only in a reduced fashion because the 12-channel coil has minimal receive field heterogeneity along the magnet z axis - the struts run parallel with the magnet axis except at the coil's rear, where they converge - and generally we want to do axial slices (along z) for fMRI. I don't yet know whether SMS-EPI would work well on the 20-channel head/neck coil on a Prisma, it's something I hope to investigate in the near future. But a 64-channel head/neck coil on a Prisma will definitely work for SMS-EPI. Better or worse than a 32-channel coil on a Prisma? I have no idea yet.

The Blipped-CAIPI sequence version 2.2 was obtained through a C2P (Core Competence Partnership) with MGH. Installation was a breeze: a single executable to port to the scanner and one click, done. The development team offers an informative but brief 7-page manual which will be useful to anyone who has read the SMS-EPI literature and has a basic understanding of how SMS works. It's not a starting point for everyday neuroscience, however. The manual mentions a .edx (protocol) file as a starting point for 2, 2.5 and 3 mm resolution scans, but in the file I downloaded for VB17A the contents didn't include it. Perhaps contact MGH if you are on another software version and you'd like a .edx file rather than building your own protocol, e.g. by recreating what you see here.


General usage issues

My immediate sense on initial testing was that overall performance of Blipped-CAIPI is quite similar to that of MB-EPI. Timing parameters and spatial resolution limits come out to be very close because they are primarily functions of the scanner hardware rather than the pulse sequence implementation. The small differences arise out of the implementation, the most significant of which is the default RF pulse type and duration. With MB-EPI one sets the duration explicitly, subject to the constraints of the RF amplifier peak output, slice thickness, cross-talk and SAR. With Blipped-CAIPI the RF duration is controlled indirectly, via a VERSE factor. More on that parameter below.

As for MB-EPI, I recommend enabling the Prescan Normalize option and instruct the scanner to save both the normalized and the raw images. The reconstruction overhead is minuscule, while a factor of two more data is a small price to pay for flexibility. However, you may prefer to acquire and use your own receive field correction map in post processing, as the Human Connectome Project did. I don't have specific recommendations today on how best to acquire your own receive field maps, but it's on the list of topics to be covered in this post series on SMS methods.

Both the Blipped-CAIPI and MB-EPI sequences use what is called in the literature the "slice-GRAPPA" reconstruction method (Setsompop et al. 2012). The "split-slice-GRAPPA" recon (Cauley et al. 2014) can be used instead by enabling the LeakBlock parameter on the Special tab of the MB-EPI sequence. In Blipped-CAIPI, however, I think the split-slice-GRAPPA is enabled automatically if one turns on conventional GRAPPA for in-plane acceleration. It's also my understanding that split-slice-GRAPPA (a.k.a. LeakBlock) should be used only when using in-plane GRAPPA with SMS. Still with me? I apologize on behalf of MRI physicists everywhere for a dog's breakfast of nomenclature. Anyway, I'll try to get more information for a recon-specific post at a later date. I'm still feeling this stuff out for myself.


Blipped-CAIPI parameter options

Single band reference images:  (Called SBref for MB-EPI.) The single band reference images option is apparently enabled on the Special card, but it is inaccessible and the single band reference images aren't actually saved on my VB17A version. I assume this is just a bug.

Dummy scans: A feature in Blipped-CAIPI is the ability to set dummy scans for the single band reference data independent of separate dummy scans inserted between the reference data and the accelerated time series (the latter is what you think of as "your data"). This assures proper T1 steady states for both the reference and time series data (in the absence of motion) even though the reference data are acquired as quickly as possible (minimum TR). With MB-EPI one can simply insert a handful of volumes of no interest and ignore these in the final time series, so there's minimal practical difference.

VERSE factor:  I have no experience with VERSE so I'm going to simply quote from the MGH manual:

Apply the Variable-rate selective excitation (VERSE) method12 to reduce peak voltage and SAR of the MultiBand pulse. When set to level 1, the VERSE method is not used and a standard [Shinnar-LeRoux] SLR pulse is played. The higher the VERSE value, the more reduction in peak voltage and SAR. This comes at a cost of slice profile distortion at off-resonance. The sequence only allows VERSE factors at which profile distortions are generally in an acceptable range. However, one should still set the VERSE level to the lowest level that will not cause RF clipping or exceed SAR limits. 
12 Conolly S, Nishimura D, Macovski A, Glover, G. (1988). Variable­ rate selective excitation. Journal of Magnetic Resonance 78: 440–458.

 And for more information, here's a paragraph from a recent review of SMS methods by Barth et al.
Variable Rate Excitation (VERSE) 

The true RF power is determined by the power integral of the RF over time. By varying the slice selection gradient with time, the k-space representation of the RF pulse is no longer mapped linearly to the time domain, and power can be reduced without modifying the slice profile. This is the principle of VERSE (30). Power reduction is achieved by slowing down k-space traversal at coordinates where most energy needs to be deposited (i.e., the peak of the [multiband] RF waveform) by temporarily reducing the amplitude of the slice selection gradient. Time lost by doing this can be recovered by speeding up at times of low RF amplitude. VERSE has great potential to reduce the power of a pulse but is very sensitive to off-resonance effects (30). Whereas a standard RF pulse off-resonance only experiences a slice shift, the sensitivity of a VERSE pulse to off-resonance varies with time due to the varying ratio between the gradient strength and the magnitude of the local field inhomogeneity, which can lead to a corrupted slice profile as demonstrated in the original study (30). In practice, the low extent to which VERSE needs to be applied to 180refocusing pulses with moderate multiband factors (MB < 4) at 3 Tesla (T), still allows an acceptable slice profile and high effective bandwidth-time product (31).

So, we should expect to see enhanced signal dropout in the usual problem regions - frontal and temporal lobes, deep brain regions - if we enable the VERSE method. In all the tests I show below I left the VERSE factor at unity, i.e. disabled. I never ran into an RF clipping or SAR-limited situation for flip angles of 45 degrees. Perhaps I'll look at the use of VERSE as a sub-component of a future post on slice-to-slice cross-talk. Until then I'll leave VERSE turned off.

SMS shift:  This is the blipped-CAIPI field-of-view (FOV) shift factor from which the pulse sequence derives its name (Setsompop et al. 2012). Here I set the SMS shift to 3 (i.e. FOV/3) based on hints from MGH and the literature. I haven't explored the consequences of different shifts. The MB-EPI sequence sets the FOV shift automatically, but the default without in-plane acceleration appears to be FOV/3.

Number of slices:  The Blipped-CAIPI sequence forces you to use an odd number of slice packets, where the number of slice packets is the total number of slices divided by the SMS factor. For example, it won't allow 60 slices when the SMS factor is 6, but 54 or 66 slices are allowed. The restriction against even multiples of the SMS factor is to reduce the potential slice-to-slice cross-talk, an issue I'll go into in depth in the next post because we also need to consider motion when considering cross-talk. (In the mean time, see Note 1.) All I can say right now is that I've not seen much cross-talk (on a stationary phantom) when using even multiples of the SMS factor with MB-EPI.

Compression factor:  This is a way to reduce the total number of effective channels in the RF coil through software combination. One gives up unique spatial information in exchange for less computation and faster reconstruction. Here's the description from the MGH manual:

Compression Factor: The amount of compression applied in a Geometric Coil Compression (GCC) scheme to reduce the number of effective coil channels and hence speed up the slice-GRAPPA reconstruction. The Compression Factor can be set to within the range of 1-4. At level 1, no compression is applied. At level 2, coil channels are compressed down by 50% (e.g. a 32-channel coil is compressed down to 16 virtual channels). At level 4, coils are compressed down to 25% (e.g. a 32-channel coil is compressed down to 8 virtual channels). Compression should mainly be used for high channel count arrays such as a 32 or 64 channel coil, where the slice-GRAPPA computation is more intensive and reconstruction time is longer. At level 2 compression (for these high channel count cases), no degradation in reconstruction performance is observed while achieving a fast image reconstruction (typically real-time in most cases). At compression level 4, some minor degradation in reconstruction performance can be observed for high SMS factors acquisitions.

Kernel size:  This is another parameter that is set automatically in the MB-EPI sequence, but with Blipped-CAIPI we have three options: 3x3, 5x3 and 5x5. This from the MGH manual:
Kernel Size: Size of the sliceGRAPPA kernel (ky × kx) used to reconstruct the images. Larger kernel sizes typically provide better reconstruction with the cost of longer reconstruction time. For low SMS factors (2-4), a 3×3 kernel size is sufficient. At higher SMS factors, a larger kernel size should be used.
I had no idea how the kernel size would affect image quality so this became the subject of preliminary testing, along with the Compression Factor as a way to influence reconstruction speed.


Blipped-CAIPI reconstruction speed

The reconstruction speed can be a major factor when deciding whether to use SMS or not. While the actual reconstruction performance depends on your software and recon hardware and mine are both rather old (VB17A with a Step IV MRIR), I thought it might be useful to give you a sense of the relative performance. I ran three throwaway tests with the following parameters fixed: 100-volume time series, 2 mm isotropic voxels, SMS factor of 6, FOV/3 CAIPI shift, TR=1000 ms, 66 total slices. I was particularly interested to see how much the kernel size and the compression factor (CF) affected reconstruction speed.

3x3 kernel, CF = 1
The first image appeared after 40 sec, and each subsequent volume took 2.2 sec to process so that the final image reconstructed 4 min 20 sec after acquisition start.

5x5 kernel, CF = 1
The first image appeared at 3 min 15 sec, long after the acquisition of all 100 images had finished. The volumes then reconstructed at a rate of ~2.6 sec/volume so that the final image reconstructed 7 min 30 after acquisition start.

5x5 kernel, CF = 2
The first image appeared after 50 sec, and each subsequent volume took ~2.2 sec to process so that the the final image appeared 4 min 25 sec after acquisition start.

The reconstruction is slow whichever way you look at it. But increasing the kernel size without also using CF > 1 makes the recon very slow indeed. Given the radical effects of CF and kernel size on reconstruction time, what can we say about image quality? Does speed come at a price we can afford to pay? Let's take a look at some specific acquisition parameter sets and then look at the effects of reconstruction parameters on image quality.


Blipped-CAIPI starting point protocols

Here are three starting protocols designed to match as closely as possible the parameters given in the previous post, for the MB-EPI sequence:

Main parameters for three starting Blipped-CAIPI protocols. (Click to enlarge.)

The full parameters are available via Dropbox in this PDF. As for the previous MB-EPI starting protocols, the number of slices for 1.5 mm isotropic resolution is insufficient to cover the whole brain. Expect to increase the TR and number of slices by about 50% for whole brain. Alternatively, you might consider increasing the SMS factor up to 8 to improve the coverage, but I haven't tested it and I would be concerned at the potential leakage artifacts that might result. (See Note 2.)

The coverage for the 2.5 mm isotropic voxel protocol is more than sufficient for whole brain when using 68 slices in a TR of 1200 ms. But if you specifically want shorter TR, down to 800 ms or so, you might consider setting the MB factor to 6 rather than 4.

The in-plane parameters are very nearly identical between Blipped-CAIPI and MB-EPI, which is to be expected given that the SMS scheme applies in the slice dimension. Small differences arise out of the duration of the SMS excitation pulse for each pulse sequence, and these lead to slight differences in minimum TE in particular. Any differences in read gradient bandwidth and echo spacing are negligible.

As for MB-EPI, the 2 mm isotropic voxel protocol for Blipped-CAIPI uses an echo spacing (of 0.70 ms) that is in the middle of the range 0.6-0.8 ms where mechanical resonances for axial slices are expected to be worst on a Trio. There is insufficient gradient strength to get below 0.6 ms, while setting the echo spacing at 0.8 ms necessitates a TE greater than 40 ms. This could be offset by setting 6/8ths partial Fourier to get back below 40 ms, but that is likely trading one potential artifact (slightly higher ghosting) for another (slightly higher dropout). In my phantom tests the ghosting from the echo spacing of 0.70 ms weren't terrible (see the example data below). But you should verify on your scanner that such an echo spacing doesn't produce show-stopping ghosts because the mechanical resonances differ from installation to installation.


Blipped-CAIPI performance on a phantom

My first task was to determine a suitable non-SMS control acquisition. I could have set up the product ep2d_bold sequence, say, with all the parameters matched to the SMS protocols except the TR, but I wanted to do a quick comparison between MB-EPI and Blipped-CAIPI and so I'm using the single band reference (SBref) images available from the MB-EPI acquisition as the standard to match. Some things to note. Firstly, the contrast in the SBref images may well be different to SMS because the TR is different. In a reasonably homogeneous gel phantom with a few air bubbles this isn't likely to be a big deal, but it does mean we can expect some intensity differences. Secondly, I want to emphasize that this is a throwaway comparison. Let me state for the record that I don't have a preference, all I have is more experience with MB-EPI than with Blipped-CAIPI. You may interpret any differences you see below any way you like, but I would caution against over interpreting anything you see. For starters I didn't even try to reproduce what I've done and you know that's a bad habit!

The following tests were conducted on an FBIRN gel phantom and with the 32-channel head coil. Each figure comprises four panels to show:
  • Top left = SBref "reference" images
  • Top right = SMS images acquired with MB-EPI
  • Bottom left = SMS images acquired with Blipped-CAIPI, processed with a 5x5 recon kernel and CF = 1
  • Bottom right = SMS images acquired with Blipped-CAIPI, processed with a 5x5 recon kernel and CF = 2
In the following section I show that the 5x5 kernel option provides the best image quality; other options are 3x5 or 3x3. But since reconstruction time is an issue, I compare here two compression factors (CF) on the basis that CF = 2 might be necessary in practice.

Let's begin by looking in the image plane, that is, in the conventional Siemens "mosaic" display. I'll use two intensity settings, the first to highlight any artifacts visible on the phantom and the second with the background scaled to reveal the N/2 ghosts and residual aliasing/leakage from the SMS reconstructions. Please note that the different number of slices in the different sequences means that there isn't necessarily a direct correspondence between the panels showing MB-EPI and Blipped-CAIPI data. The bubbles and cracks in the gel are your "anatomical references" to determine which slice is which.

There are no obvious differences visible on the phantom for 2.5 mm isotropic resolution with SMS factor 4:

Signal contrasted 2.5 mm isotropic resolution scans, SMS=4: TL: SBref. TR: MB-EPI. BL: Blipped-CAIPI, 5x5 kernel, CF=1. BR: Blipped-CAIPI, 5x5 kernel, CF=2. (Click to enlarge.)

Residual aliasing is less prominent than the N/2 ghosts, although the ghosts are sharper for Blipped-CAIPI and there is a suspicion of residual aliasing in the MB-EPI artifacts:

Ghost contrasted 2.5 mm isotropic resolution scans, SMS=4: TL: SBref. TR: MB-EPI. BL: Blipped-CAIPI, 5x5 kernel, CF=1. BR: Blipped-CAIPI, 5x5 kernel, CF=2. (Click to enlarge.)

I don't see any obvious signal level differences for 2 mm isotropic resolution and SMS factor 6:

Signal contrasted 2 mm isotropic resolution scans, SMS=6: TL: SBref. TR: MB-EPI. BL: Blipped-CAIPI, 5x5 kernel, CF=1. BR: Blipped-CAIPI, 5x5 kernel, CF=2. (Click to enlarge.)

But there are now clearly differences in the ghosts. We can use the SBref images' ghosts as our standard to recognize that the Blipped-CAIPI ghosts are crisper as well as more intense, while the MB-EPI ghosts are diffuse and exhibit multiple structures consistent with residual aliasing:

Ghost contrasted 2 mm isotropic resolution scans, SMS=6: TL: SBref. TR: MB-EPI. BL: Blipped-CAIPI, 5x5 kernel, CF=1. BR: Blipped-CAIPI, 5x5 kernel, CF=2. (Click to enlarge.)

We seem to have a choice between more intense ghosts or more intense residual aliasing. So what happens when we push to 1.5 mm isotropic resolution and SMS factor of 6? We now see that there are artifacts visible on the phantom. I've picked a few out using orange arrows for the bright artifacts blue arrows for the dark artifacts:

Signal contrasted 1.5 mm isotropic resolution scans, SMS=6: TL: SBref. TR: MB-EPI. BL: Blipped-CAIPI, 5x5 kernel, CF=1. BR: Blipped-CAIPI, 5x5 kernel, CF=2. (Click to enlarge.)

At the ghost level we again see better delineated N/2 ghosts for Blipped-CAIPI and diffuse ghosts for MB-EPI, but the artifacts clearly extend across the entire (signal-free) background in both. Scaling the background up to see the artifacts causes the background for the SBref images to saturate, indicating that the artifacts in the accelerated images are now a lot higher than for SBref, and a lot higher than for the prior 2.5 mm or 2 mm protocols:

Ghost contrasted 1.5 mm isotropic resolution scans, SMS=6: TL: SBref. TR: MB-EPI. BL: Blipped-CAIPI, 5x5 kernel, CF=1. BR: Blipped-CAIPI, 5x5 kernel, CF=2. (Click to enlarge.)


Now let's look in the slice dimension (reconstructed from the matrix of slices). This confirms no obvious artifacts for 2.5 mm isotropic resolution, SMS factor 4:

Through plane reconstruction for 2.5 mm isotropic resolution scans, SMS=4: TL: SBref. TR: MB-EPI. BL: Blipped-CAIPI, 5x5 kernel, CF=1. BR: Blipped-CAIPI, 5x5 kernel, CF=2. (Click to enlarge.)


Nothing obvious for the 2 mm isotropic resolution, SMS factor 6:

Through plane reconstruction for 2 mm isotropic resolution scans, SMS=6: TL: SBref. TR: MB-EPI. BL: Blipped-CAIPI, 5x5 kernel, CF=1. BR: Blipped-CAIPI, 5x5 kernel, CF=2. (Click to enlarge.)

But the artifacts again become apparent for 1.5 mm isotropic resolution, SMS factor 6. The orange arrow indicates a dark band on the MB-EPI image, green arrows indicate bright horizontal bands in the Blipped-CAIPI images and yellow arrows indicate phantom-shaped bright regions aliased onto the real image:

Through plane reconstruction for 1.5 mm isotropic resolution scans, SMS=6: TL: SBref. TR: MB-EPI. BL: Blipped-CAIPI, 5x5 kernel, CF=1. BR: Blipped-CAIPI, 5x5 kernel, CF=2. (Click to enlarge.)


Let's summarize things so far. The images from 2.5 mm and 2 mm protocols with SMS factors of 4 and 6, respectively, look good in qualitative terms. However, when the resolution is pushed to 1.5 mm, still with an SMS factor of 6, there are weak but visible reconstruction artifacts. For the Blipped-CAIPI sequence these artifacts are apparent whether compression factor 1 or 2 is used, suggesting that we can use CF=2 for reconstruction speed.


Effects of kernel size on image quality

I now want to go back a step and look at the kernel size. Above I selected the 5x5 kernel option throughout, while noting that the 3x3 and 3x5 options weren't as good. Here is a comparison of the 3x3 kernel to the 5x5 kernel using the 2 mm isotropic resolution protocol at SMS factor of 6. Top left is SBref, top right is MB-EPI, bottom left is Blipped-CAIPI with the 3x3 kernel and bottom right is Blipped-CAIPI with the 5x5 kernel:

Ghost contrasted 2 mm isotropic resolution scans, SMS=6: TL: SBref. TR: MB-EPI. BL: Blipped-CAIPI, 3x3 kernel, CF=1. BR: Blipped-CAIPI, 5x5 kernel, CF=1. (Click to enlarge.)

The artifacts are quite similar between the MB-EPI sequence and Blipped-CAIPI reconstructed with the 3x3 kernel. Does this mean the CMRR recon uses a 3x3 kernel? I don't know but shall endeavor to find out. The 5x5 kernel gives the crisper N/2 ghosts that better resemble the SBref "ideal" ghosts.

I also ran some 50-volume time series acquisitions that showed reduced temporal signal-to-noise ratio (tSNR) for the 3x3 kernel option:

TSNR images for 50-volume time series measurements: 2 mm isotropic voxels, SMS factor 6. Left: MB-EPI. Middle: Blipped-CAIPI, 3x3 kernel, CF=1. Right: Blipped-CAIPI, 5x5 kernel, CF=1.


The reduced tSNR comes from the spatial correlation of the artifacts across the entire image plane. Note the smoothness of the artifacts in the center panel and how they propagate across all the background regions:

Standard deviation images for 50-volume time series measurements: 2 mm isotropic voxels, SMS factor 6. Left: MB-EPI. Middle: Blipped-CAIPI, 3x3 kernel, CF=1. Right: Blipped-CAIPI, 5x5 kernel, CF=1.


So we can conclude that the cost of the smaller kernel is higher artifacts, reduced temporal stability and lower power, which doesn't look like a good trade to me. I would prefer to use the 5x5 kernel and set the compression factor to two for speed, although at this point I haven't yet done a full temporal analysis to know that setting CF=2 wouldn't similarly degrade tSNR, of course.


Blipped-CAIPI performance on a brain

And so, finally, to the brain. I want to emphasize that whatever you see here should be taken with an even larger pinch of salt than the phantom tests! It's very difficult to discriminate artifacts with brain anatomy getting in the way. But this is our first opportunity to check for new problems, such as an artifact from exquisite motion sensitivity. I'm not actively testing motion sensitivity here, however. That has to wait for a later post.

For now I offer only 3D multi-planar views for the three starting point protocols at 2.5, 2.0 and 1.5 mm isotropic resolution using compression factors of 1 and 2 (but 5x5 kernel throughout), zoomed and contrasted independently to provide the most comprehensive view of the brain:


2.5 mm isotropic resolution, Blipped-CAIPI sequence, SMS factor 4, 5x5 recon kernel, CF=1.

2.5 mm isotropic resolution, Blipped-CAIPI sequence, SMS factor 4, 5x5 recon kernel, CF=2.

2 mm isotropic resolution, Blipped-CAIPI sequence, SMS factor 6, 5x5 recon kernel, CF=1.

2 mm isotropic resolution, Blipped-CAIPI sequence, SMS factor 6, 5x5 recon kernel, CF=2.

1.5 mm isotropic resolution, Blipped-CAIPI sequence, SMS factor 6, 5x5 recon kernel, CF=1.

1.5 mm isotropic resolution, Blipped-CAIPI sequence, SMS factor 6, 5x5 recon kernel, CF=2.


What can I conclude from these views? Only that I don't see any obvious new problems requiring further investigation. Together with the phantom tests I would set my personal limits at 1.5 mm isotropic resolution and SMS factor 6. I would only push to 1.5 mm resolution if the experiment absolutely necessitated it, however. I wouldn't want to use an SMS factor greater than 6 for any protocol without a lot more testing, and right now testing a factor of 8 is low on my list of priorities.

With these starting points and a basic evaluation of two SMS sequences in the bag I'll be moving on to more detailed investigations of the consequences of slice-to-slice cross-talk and motion sensitivity.

____________________


Notes:

1.  From Setsompop et al. (2012):
"The simultaneous multi-slice method does put some constraints on the number of slices. For example, the acquisition is simplified if the total number of slices is a multiple of Rsl. A more subtle effect occurs when an interleaved slice order is used. The purpose of interleaving is, of course, to avoid exciting spatially adjacent slices in rapid succession. In a standard interleaved acquisition, adjacent slices are taken TR/2 apart in time. The interleaved Rsl = 3 acquisition has an additional constraint if one wishes to avoid having some spatially adjacent slices acquired in rapid succession. In the simultaneous multi-slice acquisition with a total of Nsl, a total of Rsl subgroups each with Nsl/Rsl slices are created. The successive excitation problem occurs between the top slice of one subgroup and the bottom slice of the subgroup above it. The problem can be avoided if the number of slices in each excitation subgroup is odd. Thus Nsl/Rsl should be an odd integer to avoid signal loss slices with imperfect slice profiles at the edge of each sub-group. If an even integer is chosen, the first slice of each subgroup will be excited right after the excitation of an adjacent slice that corresponds to the last excited slice in an adjacent slice group (from the previous TR). This leads to a signal loss from the slice crosstalk for these edge slices."

An illustration of the cross-talk is shown in Fig. 3 of Barth et al. (2016) review of SMS methods:



2.  I'll do a post at a later date that looks at the issue of SMS support in relation to the RF coil being used. A colleague observed that there are only about five discrete rings of coil elements in the Z direction for the Siemens 32-channel coil. The implication seems to be that the blipped CAIPI scheme is doing a lot (most?) of the work of separating the simultaneous slices once the SMS factor gets above 5.


Respiratory oscillations in EPI and SMS-EPI

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tl;dr   When using SMS there is a tendency to acquire smaller voxels as well as use shorter TR. There are three mechanisms contributing to the visibility of respiratory motion with SMS-EPI compared to conventional EPI. Firstly, smaller voxels exhibit higher apparent motion sensitivity than larger voxels. What was intra-voxel motion becomes inter-voxel motion, and you see/detect it. Secondly, higher in-plane resolution means greater distortion via the extended EPI readout echo train, and therefore greater sensitivity to changes in B0. Finally, shorter TR tends to enhance the fine structure in motion parameters, often revealing oscillations that were smoothed at longer TR. Hence, it's not the SMS method itself but the voxel dimensions, in-plane EPI parameters and TR that are driving the apparent sensitivity to respiration. Similar respiration sensitivity is obtained with conventional single-shot EPI as for SMS-EPI when spatial and temporal parameters are matched.

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The effects of chest motion on the main magnetic field, B0, are well-known. Even so, I was somewhat surprised when I began receiving reports of likely respiratory oscillations in simultaneous multi-slice (SMS) EPI data acquired across a number of projects, centers and scanner manufacturers. (See Note 1.) Was it simply a case of a new method getting extra attention, revealing an issue that had been present but largely overlooked in regular EPI scans? Or was the SMS scheme exhibiting a new, or exacerbated, problem?

Upper section of Fig. 4 from Power, http://dx.doi.org/10.1016/j.neuroimage.2016.08.009, showing the relationship between apparent head motion (red trace) reported from a realignment algorithm and chest motion (blue trace) recorded by a respiratory belt. See the paper for an explanation of the bottom B&W panel.

Background

To follow the full chronology please begin by reviewing the series of blog posts by Jo Etzel at WashU. Her first post was on 12th August, 2016. Jo was quickly able to demonstrate the close relationship between chest motion measured by a belt and the head movement reported by realignment. (More detailed investigations here.) These findings matched the reports by Power in http://dx.doi.org/10.1016/j.neuroimage.2016.08.009. So far so good. We explored the possibility that the transmitter frequency feedback on her Skyra scanner - a wide body scanner with gradients prone to thermal drift - might be causing the problem, but that theory fell by the wayside when I was able to reproduce the same effects on my Trio, which doesn't have transmitter frequency feedback. What else changes when one uses SMS-EPI instead of single shot EPI? The most obvious concomitant change is TR. Indeed, many people use SMS specifically to obtain a TR well below 2000 ms. Might there be a different spin history effect, perhaps one with a flip angle dependence? Again, quick tests on my Trio suggested that flip angle, hence a short TR, wasn't the root cause. That said, I'll return to the short TR because it does affect the appearance of respiratory perturbations on motion parameters.

Thinking about concomitant parameter changes led us to the next candidate explanation. As with the tendency to use a lower TR for SMS-EPI than for regular EPI, there is also a tendency to drive the in-plane gradients harder. Here's the logical progression. We start with a change in the slice dimension whereby SMS permits, say, 2 mm slice thickness and full brain coverage in a TR below 2000 ms. Next, we are tempted to improve the in-plane resolution in order to get cubic voxels. The only way to get finer resolution in-plane is to make the frequency and phase encoding gradients work harder. The SMS scheme doesn't help (or hinder very much - see Note 2) the in-plane dimension, however, and there's only so much one can drive the gradients before the total gradient area must be increased through longer application times. (If you need a refresher on gradient areas and k-space in EPI, take a look at this post and its predecessors.) Thus, a further consequence of pushing up the in-plane resolution is to increase the echo spacing in the EPI readout echo train. This means we can expect higher distortion in the phase encoding axis. Again, let me emphasize that this isn't the fault of SMS but the way in which we seek to use it: for very high spatial resolution in all three dimensions, when only the slice dimension benefits directly from the SMS scheme.

With all these issues in mind, this week we ran some tests to try to isolate the B0 modulation from other possible mechanisms, especially direct mechanical motion.


Recent tests

We used two forms of head restraint in an attempt to separate real (mechanical) head movements from modulation of B0 via magnetic susceptibility of the chest. In the first set of measurements we used a custom 3D-printed head restraint which I will describe in detail in a later post. We then repeated the measurements using standard foam padding as the head restraint. The custom head holder doesn't totally eliminate head motion, but it's considerably better at restraining the head than foam pads! We used the 32-channel head coil on a Siemens Trio running VB17A. For SMS-EPI we used the MB-EPI sequence (R014) from CMRR.

The subject conducted the same self-paced breathing task for each run. He waited until about 30 seconds into the run (so that all single band reference images had been acquired and a T1 steady state was established) then inhaled deeply and exhaled immediately, as if sighing. The deep breath-and-sigh was repeated three more times, with gaps of approximately ten seconds in between. The idea was to maximize the chest expansion but without causing too much in the way of physiologic response (via hypercapnia), as one gets with a held breath.

For each type of head restraint we ran SMS-EPI with MB=6 acceleration for axial, sagittal and coronal slices, and then ran product EPI (ep2d_bold sequence) for the same three orientations. Other parameters: voxel dimensions 2mm x 2mm x 2mm, TE = 35-36 ms (coronal slices had slightly different gradient timing to get under the stimulus limit), TR = 1000 ms, flip angle = 30 deg, 66 interleaved slices with no gap for MB=6, 11 contiguous slices with 10% gap for ep2d_bold.

For convenience you may want to download the QuickTime videos (126 MB zip file) embedded below before reading further. (For full raw data, see Note 3.) It can be quite difficult to see subtle effects in YouTube videos, whereas with the QuickTime videos you can zoom and change the looping speed (initially set to 4 fps) easily. Here I show volumes 80-120 of 200-volume data sets, zoomed to give the best view of the pertinent features. In axial slices, for instance, motion is most easily visualized in superior slices, where small movements in the slice dimension produce large changes in the amount of brain tissue present. In a future post I hope to present the full motion traces for the tests, but for now I'm afraid you'll have to make do with these.

With only foam padding we can easily detect a lot of through-plane motion as well as some in-plane motion in the axial images acquired using MB=6:



This is the sort of motion that might be seen in some of the real data sets that have been reported. Now, noting again how difficult it is to see small effects in YouTube videos, contrast the above with what happens when the subject's head is held securely by a custom restraint:


There is now very little translation visible in-plane, while the through-plane motion has also been reduced considerably. There is some residual through-plane motion, however, suggesting that either the head case is unable to reduce head-to-foot (magnet Z axis) movements as well as it does X or Y axis movements, and/or the chest movement is perturbing the magnetic field along Z and producing apparent movement effects via B0 modulation. I'll come back to this distinction below.

Next, we would like know if what is observed for MB=6 is reproducible with conventional EPI. If so, it's unlikely that the problems reported for real data are due to the SMS scheme itself. Here is the product ep2d sequence with foam padding head restraint:


The in-plane and through-plane motions are very similar to those seen in the previous MB=6 data for foam head restraint. Similarly, using the custom restraint does a good job of prohibiting in-plane (X, Y axis) head movements but does leave small through-plane (Z axis) motion, just as was seen for the MB=6 data with custom head restraint:



At this point, then, there is good evidence that the SMS scheme is not responsible for a majority of respiratory motion sensitivity. The respiratory oscillations being reported are more likely due to some other feature(s) of the acquisition.

To get a better understanding of the motion sensitivity it's useful to separate the main field direction and the slice dimension. A sagittal acquisition has the twin benefits of slicing in what is usually the least motion-contaminated direction - the subject's left-to-right (magnet X) axis - as well as preserving the phase encoding direction anterior-posterior (A-P), as for the previous axial slices. We may thus assume that sensitivity to motion, or off-resonance effects, will be similar in the A-P direction (magnet Y axis) for axial and sagittal slices, but the slice dimensions will have different motion sensitivities.

Let's go in the same order as before, starting with foam padding and MB=6 acquisition:



The through-plane motion that dominated axial slices has now largely vanished. There are two types of motion to distinguish here: translations in-plane, and changes in the amount of distortion. Motion effects on distortion are apparent as occasional stretches in the A-P (phase encoding) direction, as well as shearing in the cerebellum and spinal cord. When a custom head restraint is used to secure the head we see a big reduction in the translations in-plane, but the stretches and shearing in the A-P direction remain:



This pattern of apparent movement is consistent with modulation of the on-resonance frequency, i.e. by the expected magnetic susceptibility effects of chest motion. Changing the resonance frequency is equivalent to a phase shift in the phase encoding direction, and phase shifts produce translations in the phase encoding direction. Degradation of the shim also increases the amount of distortion, producing stretches and the appearance of shearing that is most easily discerned where the magnetic field homogeneity is already lowest, i.e. the inferior portions of the brain and the upper spinal cord.

As before, the next task is to verify that the effects seen for MB=6 are reproduced in conventional EPI, and they are. Here are the foam restraint images for sagittal slices acquired with the conventional ep2d sequence:



Using the custom head restraint again largely eliminates the head-to-foot translations while the stretches and shearing in the A-P direction remain:



Le's take a moment to reconsider the translations in the head-to-foot axis, which is the magnet Z axis. As I mentioned above, when using axial slices one cannot distinguish real movement in Z from modulation of the magnetic field along Z. The sagittal acquisitions - whether MB=6 or ep2d - reveal that the custom head restraint does a pretty good job of ameliorating real motion along Z. But there was still a rather pronounced "apparent motion" in the axial slices when using the same head restraint. Thus, it seems more likely that the residual through-plane motion effects in the axial data were due to magnetic susceptibility modulation of B0 than direct, mechanical movement. We can't be entirely sure - these data don't permit a categorical distinction of the two effects - but this explanation fits the data so far.

Shifting to a coronal prescription may provide more evidence for true mechanical motion effects in the head-to-foot direction when using a custom head restraint, if such movement exists. In the default setting provided by Siemens, the H-F axis will be the frequency encode dimension while L-R will be the phase encoding dimension. (See the post on stimulus limits for an explanation of the default gradient directions used by Siemens.) Modulation of B0 will produce only very tiny shifts in the frequency-encoded direction; the phase encoding dimension is the one most sensitive to resonance frequency shifts. So we can also predict that chest motion will produce stretches and shearing in the L-R direction in coronal EPI.

With simple foam padding there is a large amount of translation visible, here mostly in the H-F axis, that suggests direct mechanical motion is dominating the instability of MB=6 coronal images:



By using the custom head restraint we can eliminate the H-F translation to reveal more clearly the shearing effects that are most easily identified in the cerebellum, where the magnetic field homogeneity is low:



As for the sagittal data, then, holding the head securely leaves residual "apparent motion." Magnetic susceptibility effects dominate to produce distortions and shearing from modulation of B0 by chest movement.

All that remains is to verify the same behavior for conventional EPI as for SMS-accelerated EPI. Here are the product ep2d coronal images with only foam padding:



Plenty of translation as well as shearing on offer! But the custom head restraint eliminates the former to leave the latter:



We again have consistent behavior between SMS-EPI and conventional EPI. The head restraint system is the primary determinant of the motion effects seen in the time series. Residual or "apparent motion" effects left over in images acquired with good head restraint can be explained by the well-known properties of EPI. That is, by the sensitivity of the phase encoding axis (mainly) to off-resonance effects.


Summary

The first conclusion is trivial: good head restraint matters! We have always known this, but the ability of movement to dominate an EPI time series becomes more obvious the higher the resolution we try to use. Again, a moment's thought tells us this is also a trivial point. An image with voxels 1 cm on a side is already so lacking in detail that a few mm movement in any direction is unlikely to be easily detected by eye. Or, we might invert this thought and state that sub-voxel motion is hard to detect by inspection. This is an important point for those of you concerned about insidious motion contamination in resting-state fMRI in particular. Just because your motion parameters from realignment are "good" does not imply that your data are uncontaminated by motion!

But I'm getting ahead of myself. Here we are specifically concerned with SMS and any potential for greater motion sensitivity than for regular EPI. And my conclusion is that to a first approximation the motion sensitivity of SMS-EPI is not radically different to regular EPI, for matched spatial and temporal parameters.

Why, then, did people suddenly become concerned about motion in SMS-EPI? I think it's to do with the tendency to match the in-plane resolution to the slice thickness. In other words, it's the way SMS-EPI is being used rather than a problem with the SMS scheme per se. It is rare for someone to do 2 mm isotropic voxels with conventional EPI, but high spatial resolution is common once one gets a hold of an SMS sequence. Smaller voxels exhibit higher apparent motion sensitivity than larger voxels. What was intra-voxel motion becomes inter-voxel motion, and you see/detect it. Furthermore, higher in-plane resolution means greater distortion - shorter echo spacing in the EPI readout echo train - and concomitant greater sensitivity to changes in B0.

Higher spatial resolution is usually coupled with a tendency to use faster sampling (TR < 2000 ms) with SMS-EPI, and this also increases the visibility of oscillations at respiratory frequencies. Most respiration is sampled above the Nyquist frequency for TR=2000 ms, but this doesn't mean that respiratory oscillations can be readily identified in the motion parameters generated by realignment. Put another way, respiratory modulation is certainly present in your conventional EPI sampled at TR=2000 ms, whether or not you can identify it by inspection! Furthermore, the tests here with a custom head restraint indicate that you can't eliminate chest motion effects no matter what you do. They are "baked in" to your data. This is a big subject for another day.

What about additional motion sensitivity in the SMS scheme? The tests here suggest that a large fraction of the motion sensitivity in SMS is very similar to that for conventional EPI, which is not to say that SMS doesn't have additional sensitivities we should try to understand. For example, there is a possible mismatch between the single band reference data acquired at the start of the run and the accelerated time series data. For small motions - a few mm - the mismatch may not matter too much, since the spatial heterogeneity in the RF coil's receive field tends to vary quite slowly over short distances. This is something that needs to be investigated on its own. Likewise, the particular SMS reconstruction method, which may vary with the (vendor-specific) implementation and perhaps with options therein (see, for example, the Leak Block option in the CMRR sequence and literature on split-slice GRAPPA) may produce subtle motion effects in the data, some of which may be projected well beyond a slice and its neighbors.

There may be additional motion sensitivities that SMS might introduce as a further consequence of the way its used, rather than as an intrinsic property of SMS methodology. I'm thinking specifically of a potential T2 dependence, in addition to the well-known T1-dependent spin history mechanism, that may arise in species with long T2 (CSF is the prime concern) whenever the TR approaches the T2 of some signal component. This "steady state free precession" (SSFP) effect was demonstrated for serial single-shot EPI whenever coherent magnetization managed to survive the readout echo train and persists into the subsequent slice acquisition. (It is a consequence of insufficient crusher gradients at the end of a slice acquisition.) Some degree of robustness to SSFP effects may be provided by using a flip angle well below the Ernst angle. But optimal flip angle, and the possibility of SSFP effects, are both subjects for a later date. I will try to run some tests and make more detailed recommendations on flip angle selection for SMS-EPI (that is, for short TR fMRI) in the near future.

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Notes:

1.  The initial report came from Jo Etzel at WashU. She emailed me the same day that I happened to be reading Jonathan Power's latest preprint: http://dx.doi.org/10.1016/j.neuroimage.2016.08.009. In that paper, Power mentions that he observed relationships between apparent head motion, as reported by realignment parameters, and chest movement detected with a belt in several sets of SMS-EPI data he inspected. Annika Linke at SDSU then reported seeing similar oscillations in SMS data acquired on a GE Discovery MR750 scanner, indicating a problem independent of the scanner manufacturer. I subsequently received reports from sites with different Siemens platforms, including Prisma, Verio and Skyra. Thanks to all who offered data and experiences!

2.  As explained in my intro to SMS post, there is generally a need to use a longer excitation RF pulse width for SMS than for regular EPI, mostly because one is trying to define thinner slices. So the minimum TE tends to be a tad longer for SMS-EPI than regular EPI. This difference essentially disappears if one tries to define the same thin slices for regular EPI, except that this is rarely done in practice because the total brain coverage is so small.

3.  Each run comprised 200 volumes; the videos show only volumes 80-120. Data with the printed head restraint were acquired first, then the foam restraint was used. 1.4 GB zip file: https://dl.dropboxusercontent.com/u/26987499/patient.zip

Motion traces for the respiratory oscillations in EPI and SMS-EPI

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This is a follow-up post to Respiratory oscillations in EPI and SMS-EPI. Thanks to Jo Etzel at WashU, you may view here the apparent head motion reported by the realignment algorithm in SPM12 for the experiments described in the previous post. Each time series is 200 volumes long, TR=1000 ms per volume. The realignment algorithm uses the first volume in each series as the template. The motion is plotted in the laboratory frame, where Z is the magnet bore axis (head-to-foot for a supine subject), X is left-right and Y is anterior-posterior for a supine subject.

In the last post I said that there were five total episodes of a deep breath followed by sigh-like exhale, but actually the subject produced a breath-exhale on average every 30 seconds throughout the runs. (This was a self-paced exercise.) Thus, what you see below (and in the prior post) has a rather large degree of behavioral variability. Still, the main points I made previously are confirmed in the motion traces. I'll begin with the axial scan comparison. Here are the motion parameters for the MB=6 axial acquisition with standard foam head restraint (left) versus the custom printed restraint (right):

MB=6, axial slices. Left: foam restraint. Right: custom 3D printed headcase restraint

The effect of the custom restraint is quite clear. The deep breath-then-sigh episodes are especially apparent when using only foam restraint. Note the rather similar appearance of the high frequency oscillations, particularly apparent in the blue (Y axis) traces between the two restraint systems, suggesting that the origin of these fluctuations is B0 modulation from chest motion rather than direct mechanical motion of the head. We cannot yet be sure of this explanation, however, and I am keeping an open mind just in case there are small movements that the custom head restraint doesn't fix.

The product EPI acquisition of axial slices shows a similar benefit of the custom restraint:

Product EPI, axial slices. Left: foam restraint. Right: custom 3D printed headcase restraint

Furthermore, comparing the above two figures we can confirm that the overall motion sensitivity of the SMS acquisition (MB=6) and product EPI is quite similar for both foam and custom restraints, when spatial and temporal parameters are matched (except for total number of slices per TR). In spite of the task variability the peak-to-peak excursions are consistent across the restraint system being used.

I find it interesting that the realignment algorithm reports similar motion for product EPI, with only 11 total slices, as for SMS-EPI with 66 slices. The total anatomical content in the 11 axial slices located at the top of the head is markedly lower than the near full brain coverage of the 66 slice acquisition. Yet there doesn't appear to be a large cost for the poorer coverage. Perhaps there is slightly greater low frequency drift being reported for product EPI than SMS-EPI when using foam padding. The rather similar drifts apparent when using custom restraint would suggest that gradient heating isn't the cause. It's something I will look into in more detail separately, since Jo has kindly re-run the motion correction using a subset of the full SMS-EPI data.


Next I want to consider the coronal comparisons, because we retain the issue of low brain coverage and low anatomical content for the product EPI images. The 11 slices of the product EPI acquisition were positioned over the occipital cortex. Here is the MB=6 coronal acquisition with standard foam head restraint (left) versus the custom printed restraint (right):

MB=6, coronal slices. Left: foam restraint. Right: custom 3D printed headcase restraint

The excursions in pitch (red traces) and yaw (brown traces) in particular, appear to be larger for the coronal than the previous axial prescriptions, whether using foam or custom head restraint. Recall that the coronal acquisitions used L-R phase encoding and so perturbations of B0 change the distortion in that dimension to produce shearing. This clearly violates the rigid body assumption of the realignment algorithm and I can only assume that we are seeing some consequence of this reflected in the motion parameters. A good issue for someone with a lot of image processing expertise to dig into, or comment on. For the time being I am going with the hypothesis that the larger fluctuations for coronal than axial slices when using the custom restraint are due primarily to a greater sensitivity to B0 perturbation by chest movements when using L-R phase encoding in coronal slices. But I am leaving open the possibility of uncorrected direct motion.

The coronal data acquired with product EPI don't show the same systematic effects in pitch and yaw as the SMS data. Instead the traces are rather messy:

Product EPI, coronal slices. Left: foam restraint. Right: custom 3D printed headcase restraint

Is the absence of any dominant directionality in the traces a consequence of the reduced coverage in the product EPI scans? For now I'm assuming this is so. More on this in the next post.


Finally we can consider the sagittal scans. As a reminder, the slice direction is orthogonal between sagittal and axial slices, but they share a common phase encoding direction (anterior-posterior, or magnet Y axis). Differences between axial and sagittal data should thus reflect primarily differences in the slice dimension sensitivity to head motion and B0 modulation. Here are the motion parameters for the MB=6 sagittal scans with standard foam head restraint (left) versus the custom printed restraint (right):

MB=6, sagittal slices. Left: foam restraint. Right: custom 3D printed headcase restraint

When using custom head restraint the high frequency oscillations that were seen in the MB=6 axial scans are very similar to the oscillations in the MB=6 sagittal data, again consistent with B0 modulation from chest movements and implying a primary sensitivity in the phase encoding direction. What about other features that may differ between axial and sagittal data? There is a suggestion of reduced low frequency, drift-like motion for the sagittal scans. Until I've repeated the experiment I'd have to concede that gradient heating is the most likely explanation. Still, I wouldn't exclude the possibility just yet that perhaps the sagittal prescription has a lower sensitivity to both motion and B0 modulation from respiration, given that for axial scans we are slicing along the main magnetic field (Z) axis. It's something I plan on investigating.

The eleven sagittal slices acquired with product EPI have greater anatomical content than either the axial or coronal counterparts because I positioned them right down the midline. While there may still be issues with limited coverage compared to the full brain coverage permitted with SMS-EPI, we might expect a greater similarity with the MB=6 acquisition. Here are the sagittal EPI data:

Product EPI, sagittal slices. Left: foam restraint. Right: custom 3D printed headcase restraint

To my eye there is more similarity between the motion traces produced for sagittal product EPI and MB=6 than there was for either axial or coronal. Again, with N=1 we can't be sure, but this is an interesting starting point for future investigations where total brain coverage might be an important variable in the protocol. And we can't forget that the shearing produced in inferior portions of the brain will violate the rigid body assumption, as for the coronal data.


Final thoughts

In spite of the single set of tests presented here, the most important findings as reported in the last post are confirmed in the motion traces. The custom head restraint makes a truly massive difference to overall motion sensitivity. But the use of SMS-EPI does not ipso facto enhance the motion sensitivity. For matched spatial and temporal resolution we see just as much motion sensitivity for conventional EPI. Having reduced the head motion there is the residual issue of fluctuations at respiratory frequencies, caused by main field modulation. The sensitivity to both direct motion and respiratory effects varies considerably with assignment of the logical axes. No surprises there.

These results offered a few interesting new thoughts to guide future tests. How much does the total brain coverage affect realignment algorithm efficacy? When distortion effects clearly violate the rigid body assumption, what are the consequences when the head moves or when respiratory effects produce shearing? These are questions for another day. For now, though, I contend that we have enough evidence to suggest that most if not all fMRI studies - especially those using high spatial resolution - need to be doing even better with their head restraint, and that if one is contemplating a high-resolution fMRI experiment then a deeper consideration of respiratory effects is also warranted.

Thanks again to Jo Etzel for stimulating the current investigation with her own observations, and for all her stellar work since.


Use of split slice GRAPPA (aka Leak Block) for SMS-EPI reconstruction

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Accurate separation of the simultaneously acquired slices is one of the bigger limitations of the SMS-EPI method, compared to the processing used for conventional multislice EPI. The default SMS reconstruction, as used in my two introductory posts on the SMS sequences from CMRR (MB-EPI) and MGH (Blipped CAIPI), is a slice dimension adaptation of the GeneRalized Autocalibrating Partial PArallel (GRAPPA) method that was originally applied in-plane to acceleration of the phase encoding direction. It's not essential to understand the GRAPPA method applied in-plane for the purposes of understanding this post or for SMS reconstruction more generally. But if you're curious I wrote a brief introduction to in-plane GRAPPA in 2011. That post was specifically concerned with motion sensitivity of (in-plane) GRAPPA. I'll be looking in more detail at the motion sensitivity of SMS in a future post. In this post I want to compare the standard SMS reconstruction - what is generally termed Slice GRAPPA - with an alternative known as Split Slice GRAPPA. The latter option is termed "Leak Block" in the CMRR pulse sequence, MB-EPI.


What's the concern?


CMRR's parameter nomenclature offers a strong clue to the problem. In conventional EPI reconstruction we use a 2D Fourier transform (FT) which produces some amount of ringing. We also use slices that have some degree of cross-talk to neighboring slices, arising out of the limitations of frequency selectivity. So, while we think of voxels as perfect little rectangles or cubes, in reality they are blurry beasts that spread their signal into adjoining voxels because of a non-rectangular point-spread function (PSF). The dimensions we assign a voxel are entirely nominal.

With SMS we have a broader spatial problem than just non-cubic PSF. Separation of the simultaneous slices can leave signal in an incorrect position that is quite some distance from where it is supposed to be. It's a longer length scale error than the simple PSF of a voxel. Let's suppose we acquire four 2 mm slices simultaneously, 84 total slices. In one SMS acquisition we will have four slices separated by one quarter of the total slice dimension extent of 168 mm, or about 42 mm (assuming no additional inter-slice gap). Do a quick thought experiment. Imagine that in the first slice there is a very strong activation and nothing in the other three. If there is a large residual spatial error arising from poor SMS separation then we might start seeing this activation projected 4.2, 8.4 or even 12.6 cm from where it should be! And how would we know that the distant activation sites were erroneous?

This slice leakage, as it's usually called in the literature, may be strongest for simultaneously acquired neighbors but may extend throughout the slice dimension, between simultaneously acquired slices that might be quite far apart in anatomical space. And, as the thought experiment illustrates, one might assume that distant leakage would be harder to spot than the conventional cross-talk between successively acquired slices in conventional multislice EPI, or errors arising from the PSF more generally. The PSF can usually be interpreted as a local phenomenon, with errors decreasing monotonically from a voxel. Not so with SMS slice separation, meaning there is more risk of interpreting a false positive remote from the true activation site.

At this point we can recognize that reducing leakage is a noble, perhaps essential, goal. As usual with MRI, however, there's a catch. Reducing leakage using the Split Slice GRAPPA reconstruction may come at the cost of increasing in-plane artifacts. The overall (total) artifact level might be higher, too. I'll go into these issues in some detail below. The goal of this post is to perform a rudimentary assessment of the artifacts and determine the circumstances when Split Slice GRAPPA might be preferred over the conventional Slice GRAPPA reconstruction. For the CMRR sequence this amounts to whether or not to enable the Leak Block option.


What does the literature tell us?


"A couple of months in the laboratory can frequently save a couple of hours in the library." This aphorism is attributed to the chemist Frank Westheimer, in 1988. I first came across it courtesy of the Unix command fortune, which we used run automatically after logging in to a Sun workstation back in the 17th century (or thereabouts). It has been updated for the 21st century by Runyon's corollary: "A couple of hours on the Internet can frequently save a couple of minutes in the library."Even so, reading the literature before heading down to the scanner can still be a useful exercise, provided one takes the precaution to disable e-mail and Twitter first.

The paper that introduced the Split Slice GRAPPA reconstruction for SMS-EPI is by Cauley et al. (2014). I've quoted below some of the most important points from the paper, beginning with a brief review of the history of SMS then highlighting the motivation for Split Slice GRAPPA over Slice GRAPPA. My clarifications are in [square brackets] and I truncated some sentences... to remove formulas that we don't need for this post:
SMS is a promising parallel imaging modality that has been shown to work well when the simultaneously acquired slices have substantial distance between them. However, for brain imaging the smaller FOV along the slice direction limits the distance factor and the simultaneously acquired slices are more difficult to separate.
Controlled aliasing (CAIPI) techniques have been introduced in (9) to perform shifts across the slices to more easily unalias the accelerated data.

A recent work (14) examined using blipped-CAIPI to achieve spatial shifts in the PE [phase encode] direction, between simultaneously excited slices to avoid voxel tilting artifacts. This has enabled SMS acquisitions with high acceleration factors with a low g-factor penalty; allowing for significant gains in the temporal efficiency of diffusion imaging and fMRI acquisitions.

The blipped-CAIPI scheme is now used by default in both the CMRR and MGH sequences, so the issue of tilted voxels is no longer a concern. Let's go on.
Similar to [in-plane] GRAPPA (3), the SG [Slice GRAPPA] method uses training data to fit a linear model that is used to unalias the simultaneously acquired slices. With SG, distinct kernels are used to unalias each of the simultaneously acquired imaging slices. It was illustrated in (14) that the fitted SG kernels showed a strong dependence on the static coil sensitivity profiles and not on the training data image contrast. This is a desirable property that allows the SG kernels to be used to accurately unalias SMS data that can have different contrast from the training data, e.g. in the case of diffusion encoding. However, in this work we will show that when using high slice acceleration together with in-plane accelerations the contrast independent property of the SG kernels will suffer. This results in an increased dependency of the kernels on the training data image contrast and causes increased signal leakage between the unaliased simultaneously acquired slices.

While the standard SG kernel fitting produces kernels that minimize the image artifact, the SP-SG [Split Slice GRAPPA] method takes a more balanced approach. The SP-SG method simultaneously minimizes errors coming from both image artifacts and leakage. This is accomplished by forming a new kernel fitting objective function to consider the importance of both sources of error.

In particular, the robustness of the fitting kernel across b-values is demonstrated through reductions in artifacts and improved SNR. Based on this work, the SP-SG method has the potential to enable a more robust and less artifact prone SMS acquisitions at high acceleration factors. This should facilitate further improvements in temporal efficiency of fMRI and diffusion imaging acquisitions.

...reducing the total artifact without placing restrictions on the intra- and inter-slice artifacts can lead to a dependency on artifact cancellations. With the SG method the intra- and inter-slice artifacts might be arbitrarily large but combine to help reduce the total artifact...

Note that the SP-SG formulation will result in higher total artifact error (5). That is, for SG reconstruction each convolution matrix will directly contribute toward reducing the RMSE [root-mean-square error]while no condition is placed on the inter-slice artifact... For SP-SG reconstruction we attempt to limit the influence of inter-slice artifacts... This additional condition for SP-SG can increase the kernel fitting RMSE with respect to the SG objective. However, with the SG method, using all of the slice convolution matrices to improve the kernel fitting RMSE can result in artifacts during the application of those kernels to images with different contrasts. This is caused by changes in the inter-slice leakage that no longer contribute toward reducing RMSE. By limiting the dependency on inter-slice leakage artifacts during the training process the SP-SG method is less vulnerable to produce artifacts based upon image contrast change.

So the Slice GRAPPA reconstruction might be sub-optimal for diffusion-weighted imaging (DWI), where a non-DW scan, often referred to as a b=0 image, is typically used to generate the reconstruction kernel before the kernel is applied to all the DW images in the data set.

There's an additional factor, another potential difference between SMS used for DWI and SMS used for fMRI. For DWI we almost always use in-plane acceleration to render the echo time (TE) acceptably short. If we also want to use SMS then we would be under-sampling two of the three spatial dimensions. How might in-plane acceleration interfere with SMS? Back to Cauley et al.
In-plane acceleration reduces the effective amount of PE shift that can be applied in a SMS acquisition. In this work, a FOV/3 shift was used within the in-plane accelerated “reduced” FOV [field-of-view]. This corresponds to a FOV/6 shift in the full FOV [for acceleration factor of R=2 in-plane], which results in relatively small distances between the aliased voxels. Therefore, with our combined acceleration approach, we expect the contrast dependency property of the SG kernel to be similar to MB=6 acquisitions with no in-plane acceleration (and significantly larger than the MB=3 only case).

In fMRI acquisitions the image contrast does not change significantly for a time-series. Therefore, the total artifact error of the standard SG method should be lower than that from the SP-SG method. However, the SG method will still result in more signal leakage because of the kernel fitting dependency.

For example, in fMRI applications it might be desirable to sacrifice intra-slice artifact performance to reduce the inter-slice leakage artifact. This can be viewed as a specificity and sensitivity trade-off. The inter-slice leakage artifact can cause a reduction in specificity by creating displaced false positives due to signal leakage. On the other hand, the intra-slice artifact will cause a spatially varying signal attenuation/amplification for a given slice. This will affect the sensitivity to activation detection and with large attenuation false negatives can occur. However, small modulation on signal level is not particularly harmful while a small leakage can result in a large displacement of detected activation. This is particularly evident when the acquisition is physiological noise dominated. In this regime, the relatively small attenuation/amplification due to the intra-slice artifact will affect both the signal and noise equally and there should be no net effect on the sensitivity to activation.


Let's turn our attention to another paper: Evaluation of 2D multiband EPI imaging for high-resolution, whole-brain, task-based fMRI studies at 3T: Sensitivity and slice leakage artifacts, by Todd et al. (2016). They assessed leakage for these parameter combinations:
MB factors of 1, 2, 4, and 6, combined with in-plane GRAPPA acceleration of 2 × (GRAPPA 2), and the two reconstruction approaches of Slice-GRAPPA and Split Slice-GRAPPA. 

Unfortunately, the one condition not tested was SMS-only, i.e. SMS without in-plane GRAPPA, most likely for the convenience of predicting false positive locations in a consistent manner, as will be explained below. Never mind.

The aim of the Todd study was to determine leakage via projection of false positives from the actual locations of activity, for a simultaneous visual and motor task: a 10 Hz flashing checkerboard and finger-to-thumb tapping. It's the real version of the thought experiment I did above. First, they established the true activation sites in the visual and motor cortices, and in the cerebellum. The locations of false positives were then determined using seed voxels in the true activation locations, as follows:
To determine if a false-positive activation occurred at an aliased location, the voxel with the largest t-score value for all activation clusters defined by SPM were considered as “seed” voxels. For each “seed” voxel chosen, the t-score values in the single voxel at the possible alias locations were evaluated. The detection of a false positive had to satisfy both criteria that (1) the single voxel at the exact alias location had a t-score value larger than the significance threshold corresponding to p < 0.001 (uncorrected), and (2) a 3 × 3 × 3-voxel volume at the alias location in the three other multiband scans did not have any voxels with t-score values that exceeded the significance threshold. The second criterion was designed to guard against the possibility that the aliased location could fall within a region of true positive activation.
How did they determine all possible aliased locations? This is where the consistent use of in-plane GRAPPA enters the picture:
The expected alias locations of a particular voxel were inferred from the multiband factor, in-plane GRAPPA factor, and in-plane CAIPI-shift. Since all multiband factors used in-plane GRAPPA 2 and in-plane CAIPI-shift FOV/3, there are two alias locations per simultaneously acquired slice, one shifted by (FOV/3)*m and one shifted by (FOV/3)*m + FOV/2, where m is the number of simultaneously excited slices away from the original slice.
(For anyone attempting to repeat this study, please see Note 1 for an important caveat regarding the FOV shift amount.)

Todd et al. observed 106 false positives for Slice GRAPPA versus only 11 for Split Slice GRAPPA:
When using Slice-GRAPPA reconstruction, evidence of false-positive activation due to signal leakage between simultaneously excited slices was seen in one instance, 35 instances, and 70 instances over the ten volunteers for the respective accelerations of MB 2 × GRAPPA 2, MB 4 × GRAPPA 2, and MB 6 × GRAPPA 2. The use of Split Slice-GRAPPA reconstruction suppressed the prevalence of false positives significantly, to 1 instance, 5 instances, and 5 instances for the same respective acceleration factors.

After accounting for multiple comparisons they estimate that up to seven false positives might arise by chance. So, the Split Slice GRAPPA seemed to work rather well, whereas leakage was a problem for Slice GRAPPA once the SMS factor was 4 or higher and when also using in-plane GRAPPA. The aliased location of some of the false positives with Slice GRAPPA is important to note, too:
False-positive activation was seen not only in the simultaneously excited slice immediately adjacent to the true positive origination slice, but also sometimes in a location two slices away. Of the 106 instances of false-positive detection, there were 22 cases in which false positives were seen in more than one alias location. There were no instances of false-positive activation being detected in a location three slices or more away from the true activation origin.

Let's sum up. The main recommendations arising from Todd's study are as follows:
...false-positive activation arising when BOLD signal changes due to true positive activation in one slice leak into other simultaneously excited slices can occur when using multiband factors of 4 or higher combined with in-plane accelerations,

A very conservative approach for high-resolution whole-brain fMRI studies would be to use multiband acceleration factor 2, in-plane GRAPPA acceleration factor 2, and Split Slice-GRAPPA reconstruction.

This is all good to know. But we don't yet know what might be appropriate if we disable in-plane GRAPPA and use just SMS acceleration. We also have a vast parameter space to explore, as Todd et al. caution:
It is important to point out that most 3 T studies, which use more conventional resolutions of 2–3 mm, do not typically employ in-plane accelerations, nor is the need for it significant given the lower resolutions of those studies.
...the effectiveness and optimization of the CAIPI shift factor was not evaluated for the experimental conditions used in this work and the use of different shift factors may have altered the findings presented here. 

I think we have a starting point. I'll keep the spatial resolution reasonably high, at 2 mm isotropic - Todd et al. used 1.5 mm cubic voxels - and stick with the default CAIPI shifts (as described in Note 1).


Throwaway tests on a Trio


I currently have version R014 of MB-EPI installed on my TIM/Trio running VB17A software. Todd et al. used version R011a of the same sequence. (See Note 1 for an important change in the default CAIPI shift in R012 and later.) I used a 32-channel receive-only head coil and an FBIRN gel phantom. The fixed acquisition parameters were: voxel size = 2mm isotropic, TE = 36.4 ms, echo spacing = 0.7 ms, read bandwidth = 1814 Hz/pixel, RF duration = 8200 us, axial slice prescription with A-P phase encoding, 7/8ths partial Fourier in the phase encoding dimension. The number of slices, TR and SMS factor were then varied as described below.

For the remainder of this post I'm going to switch to using the CMRR nomenclature. That is, in the MB-EPI sequence the Split Slice GRAPPA reconstruction is activated by enabling the Leak Block option. Otherwise, when Leak Block is off we are using the default reconstruction, i.e. Slice GRAPPA. I'm also going to use the Siemens nomenclature for in-plane acceleration. The in-plane acceleration method will always be GRAPPA (the other Siemens option being mSENSE) while the degree of in-plane acceleration is given by the iPAT factor. This creates one more parameter option to consider: the way the auto-calibration scans (ACS) are acquired for in-plane GRAPPA at iPAT = 2. The Siemens default is a single shot ACS, whereas distortion effects are matched properly only when using 2-shot (interleaved) ACS. See Note 2 for more information on the ACS options.

Artifacts visible in signal regions:

We were warned by Cauley to expect more in-plane artifacts when using Leak Block, so I opted to begin with an evaluation of in-plane artifacts before moving on to an assessment of leakage artifacts between slices. Todd concluded that an SMS factor of 4 or more, with iPAT = 2, was "accelerating too far." For the initial tests I wanted to explore the extremes. I was also interested to know if the potential for distortion-related artifacts from 1-shot ACS might be an issue overlooked by Todd et al., since they used the Siemens default for in-plane GRAPPA. I therefore tested single shot ACS versus a 2-shot segmented ACS that can be selected with a sequence flag, for SMS factors of 3 and 6:

SMS = 3, TR = 2000 ms, 66 interleaved slices. Top-left: no iPAT, Leak Block off. Top-right: iPAT = 2 with 1-shot ACS, Leak Block off. Bottom-left: iPAT = 2, segmented 2-shot ACS, Leak Block off. Bottom-right: iPAT = 2, segmented 2-shot ACS, Leak Block enabled. (Click on the image to enlarge.)

SMS = 6, TR = 1000 ms, 66 interleaved slices. Top-left: no iPAT, Leak Block off. Top-right: iPAT = 2 with 1-shot ACS, Leak Block off. Bottom-left: iPAT = 2, segmented 2-shot ACS, Leak Block off. Bottom-right: iPAT = 2, segmented 2-shot ACS, Leak Block enabled. (Click on the image to enlarge.)

There is clearly an interaction, leading to artifacts, for the case of SMS = 6, iPAT = 2 and use of Leak Block reconstruction. Disabling Leak Block (bottom-left and top-right panels in the above figure) eliminated the artifacts for both 1-shot and 2-shot ACS. Furthermore, to save space I displayed only the results for 2-shot segmented ACS when using iPAT = 2 and Leak Block enabled (bottom-right), but the results were very nearly identical for single shot ACS, for both SMS of 3 and 6. The consistent results suggest that for a spherical phantom with minimal structure - just a few air bubbles - there is no major interaction of the ACS scheme with the Leak Block reconstruction. Rather, it is the interaction of the Leak Block reconstruction with the total acceleration - iPAT = 2 and SMS factor 6 - that produces the artifacts. These result might not hold in a heterogeneous brain but for phantom testing purposes, given the similar performance of 1-shot and 2-shot ACS above, from this point on I opted to use just the 1-shot ACS. (See Note 3 for one additional test for iPAT = 3.)

In the next set of tests I sought to establish the point at which artifacts are introduced as the SMS and iPAT factors are increased. Here are the tests for SMS factors of 4, 5, and 6, with iPAT = 1 and 2:

SMS = 4, TR = 2000 ms, 68 interleaved slices. Top-left: no iPAT, Leak Block off. Top-right: no iPAT, Leak Block on. Bottom-left: iPAT = 2, Leak Block off. Bottom-right: iPAT = 2, Leak Block enabled. (Click on the image to enlarge.)

SMS = 5, TR = 2000 ms, 60 interleaved slices. Top-left: no iPAT, Leak Block off. Top-right: no iPAT, Leak Block on. Bottom-left: iPAT = 2, Leak Block off. Bottom-right: iPAT = 2, Leak Block enabled. (Click on the image to enlarge.)

SMS = 6, TR = 1000 ms, 66 interleaved slices. Top-left: no iPAT, Leak Block off. Top-right: no iPAT, Leak Block on. Bottom-left: iPAT = 2, Leak Block off. Bottom-right: iPAT = 2, Leak Block enabled. (Click on the image to enlarge.)


If you have a very good eye then you might just pick up subtle intensity variations introduced by iPAT = 2 and SMS = 5 when using Leak Block. The combination iPAT = 2, SMS = 6 and Leak Block produces clear in-plane artifacts. The corresponding single band reference (SBref) images - not shown - are artifact-free, however, confirming that we are indeed seeing an interaction of the Leak Block SMS reconstruction with the in-plane acceleration. (See Note 4 for a comparison of the MGH sequence, Blipped CAIPI to CMRR's MB-EPI. They perform similarly.)

Slice leakage:

What about the effect of Leak Block on slice leakage? What benefit might we get for the cost of the in-plane artifacts seen above? I'm going to use the simplest analysis I can think of: inspection. Leakage artifacts are easily seen in regions that should be noise if one positions the slices to one side of the phantom. It turns out that the leakage patterns are quite periodic, reflecting the SMS factor being used, and they extend in regular fashion off into the noise.

To help you identify the different artifact sources, consider this matrix of expected artifacts that corresponds to the panels in the three figures below: 

Artifact types expected in the next three figures. N/2 ghosts are intrinsic to EPI acquisition and always present. Slice leakage is expected for Slice GRAPPA reconstruction of SMS-EPI but minimally for Split Slice GRAPPA (i.e. Leak Block) reconstruction. Residual aliasing is a feature of in-plane GRAPPA (i.e. iPAT).


Here are views of the leakage artifacts corresponding to the three tests for SMS factors of 4, 5, and 6, with iPAT = 1 and 2. The slice positions are slightly different than in the three figures above, and the image contrast has been optimized for the leakage artifacts, but otherwise these three composite figures match the three composite figures above:

SMS = 4, TR = 2000 ms, 68 interleaved slices. Top-left: no iPAT, Leak Block off. Top-right: no iPAT, Leak Block on. Bottom-left: iPAT = 2, Leak Block off. Bottom-right: iPAT = 2, Leak Block enabled. (Click on the image to enlarge.)

SMS = 5, TR = 2000 ms, 60 interleaved slices. Top-left: no iPAT, Leak Block off. Top-right: no iPAT, Leak Block on. Bottom-left: iPAT = 2, Leak Block off. Bottom-right: iPAT = 2, Leak Block enabled. (Click on the image to enlarge.)

SMS = 6, TR = 1000 ms, 66 interleaved slices. Top-left: no iPAT, Leak Block off. Top-right: no iPAT, Leak Block on. Bottom-left: iPAT = 2, Leak Block off. Bottom-right: iPAT = 2, Leak Block enabled. (Click on the image to enlarge.)

The benefit of Leak Block (right-hand panels) is obvious. All the left-hand panels contain artifacts consistent with inter-slice leakage. The artifacts look like the wet rings left by beer glasses on a bar! Maybe someone should contrive the acronym COASTER for the next version of Split Slice GRAPPA. (See Note 5.)


Conclusions


In this post I considered only axial slices on a stationary phantom. The performance of any particular SMS, iPAT and Leak Block parameter combination will likely differ as soon as there is significant sample/subject motion. And, since head motion is anisotropic, performance will also vary with the assignment of the slice and phase encode axes relative to the brain. (See the previous post for some examples.) Indeed, the assignment of the slice and phase encode axes is important even in the absence of motion because the layout of the detector loops in the 32-channel head coil is asymmetric, and we should therefore expect that performance of both SMS and iPAT will change if coronal or sagittal slices are used.

Given the caveats, what can we say with any certainty? As far as they go, my observations on a phantom are consistent with the findings of Cauley et al. and Todd et al. in brains. The combination of SMS = 6 and iPAT = 2 is at or past the limit of what can be done with axial slices using a 32-channel coil at 3 T. Image artifacts become quite prominent when using Leak Block (aka Split Slice GRAPPA) with SMS = 6 and iPAT = 2. If SMS = 6 and iPAT = 2 are deemed essential then I would suggest not using Leak Block. Stick with the default Slice GRAPPA reconstruction. Alternatively, if you want to use SMS = 6 and you don't need iPAT then by all means use Leak Block. Or, if you decide that iPAT = 2 and Leak Block are essential then I would reduce the SMS factor below 6. Todd suggests using an SMS factor below 4 if iPAT = 2.

As it happens, I'm not a big fan of iPAT for fMRI because of its motion sensitivity. (See posts here and here.) There are recent developments that aim to improve the robustness of the ACS to motion in GRAPPA, such as FLEET, but these methods aren't yet widely available for conventional EPI or SMS-EPI. Methods like FLEET attempt to reduce the motion sensitivity of the ACS, but as yet I've not seen any methods that address the potential for mismatch between the ACS and the under-sampled time series. So my preference for fMRI would be to eliminate iPAT and use an SMS factor up to 6, with Leak Block enabled.

For diffusion-weighted imaging, on the other hand, the use of iPAT is all but required in order to keep TE reasonable. While I have yet to run any specific tests for DW-SMS-EPI, the results above suggest that a moderate SMS factor of 2-4, with  iPAT = 2 and Leak Block enabled should be acceptable. I'll present the results of DW-SMS-EPI tests in a future post. In the next post I want to assess the impact of motion on SMS-EPI for fMRI applications.

Until then, Happy New Year!

_______________________


Notes


1.  From Todd et al.:
MB factors 2, 4, and 6 all used an in-plane CAIPI shift of FOV/3 that was automatically set by the sequence.
This is because they used CMRR's sequence version R011a for which a CAIPI factor of FOV/3 was the default. But this was changed from R012 on, when for GRAPPA with R=2 acceleration the CAIPI factor was increased to FOV/4. It is still FOV/3 when in-plane GRAPPA isn't used, however. See the R014 release notes for more details. In MGH's Blipped CAIPI the default is FOV/3 but the factor can be changed by the user.


2.  The single shot ACS uses a k-space increment in the phase encode direction that corresponds to the full FOV; no aliasing. Being single shot, it's fast and is somewhat robust to motion. But it means there is a difference in the distortion of the ACS and the under-sampled EPI data that comprise the fMRI time series because the latter use a k-space increment that is twice as big, resulting in a total echo train length half as long (and a FOV half as big, creating aliasing). Such a mismatch in distortion properties creates artifacts in regions of strong magnetic susceptibility gradients.


3.  I did a comparison of MB=3 to MB=6, using both iPAT=2 and iPAT=3, just in case the interaction of high MB factor and iPAT=2 is a special case. It's not. Top-left: SBRef images from MB=3, no iPAT, as a gold standard. Top-right: MB=3, iPAT=2, segmented ACS, Leak Block on. Bottom-left: MB=6, iPAT=2, segmented ACS, Leak Block on. Bottom-right: MB=6, iPAT=3, segmented ACS, Leak Block on. Only MB=3, iPAT=2 is artifact-free. Accelerating to higher rates of MB x iPAT isn't advisable.




4.  I was able to produce similar artifacts using the MGH sequence, Blipped CAIPI. It uses Split Slice GRAPPA reconstruction by default when iPAT acceleration is enabled.

As for MB-EPI, iPAT alone was artifact-free, and only the interaction of iPAT and Split Slice GRAPPA produces artifacts. Here are the results for SMS = 6:


Top-left is MB-EPI with iPAT = 2, Leak Block off. Top-right is MB-EPI with iPAT = 2 and with Leak Block enabled. Bottom-left is Blipped CAIPI, no iPAT. Note the absence of artifacts. Bottom-right is Blipped CAIPI with iPAT = 2, and now Split Slice GRAPPA recon is being used we see artifacts that are somewhat similar (but clearly not identical) to those with MB-EPI, iPAT = 2 and Leak Block enabled. I wouldn't expect identical performance because there are a number of other implementation differences between MB-EPI and Blipped CAIPI. The important point to recognize is that the use of Split Slice GRAPPA (or Leak Block, if you prefer) instead of Slice GRAPPA reconstruction has fundamental consequences regardless of the particular implementation. The artifacts produced by the interaction of SMS, in-plane GRAPPA and Split Slice GRAPPA reconstruction are a feature, not a bug, in accord with the comments in Cauley et al. (2014).

5.  Okay, fine. I'll start. Control Of Awful Separation To Eradicate Replicas. COASTER.


References


Cauley SF, Polimeni JR, Bhat H, Wald LL, Setsompop K.
Interslice leakage artifact reduction technique for simultaneous multislice acquisitions.
Magn Reson Med.72(1):93-102 (2014).
doi: 10.1002/mrm.24898

Todd N, Moeller S, Auerbach EJ, Yacoub E, Flandin G, Weiskopf N.
Evaluation of 2D multiband EPI imaging for high-resolution, whole-brain, task-based fMRI studies at 3T: Sensitivity and slice leakage artifacts.
Neuroimage. 124(Pt A):32-42 (2016)
doi: 10.1016/j.neuroimage.2015.08.056

"Power plots" of respiratory effects in EPI

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This will be brief, a simple demonstration of the sort of features visible in a "Power plot" of an EPI time series. The goal is to emphasize that chest motion produces apparent head motion effects in typical analyses. Here the subject's head was held very firmly in the 32ch coil of my Siemens Trio using a custom printed head case. See the posts from October last year for more details. In this test the subject inhaled to near maximum and exhaled immediately, repeating the procedure every 30 seconds or so in a self-paced manner. The subject breathed normally otherwise. Critically, note that no breaths were held.


What we see are two striking features. First, there is banding with a period of approx 30 seconds, and the bright bands correspond with apparent head movement reported as framewise displacement (FD) in the top red trace. (TR is 1700 ms.) Some of this may be real head movement, but a lot arises from chest displacements modulating the magnetic field. This is the feature I want to emphasize. We need to be aware that not all sources of frame-to-frame variation reported by a volume registration (aka motion correction) algorithm are necessarily actual head motion. Last October I showed in a series of simple demonstrations how chest motion produces shearing and translations of EPI signals in a manner consistent with perturbation of magnetic field, rather than head motion per se. It's important for you to distinguish these two phenomena because the volume registration algorithm cannot differentiate them. It does its best to match volumes no matter the source of differences.

The second feature in the plots above I'm not going to get deep into here. It's for another day. But it's pretty hard to miss the dark bands that follow tens of seconds after each bright band. Notice that the dark bands don't tend to coincide with increased FD. That is, the origin of the dark bands isn't actual or apparent head motion but something else. They come from changes in BOLD signal as the arterial CO2 changes. This is the part of the "physiologic noise" that people try to model with things like RETROICOR and RVT, or from end-tidal CO2 measurements. Here, the perturbation in BOLD signal is driven by the strange breathing task, but it's not motion or motion-like. It's real physiology in the brain.

That's all for now! More posts on this stuff in the coming weeks.



Major sources of apparent head motion in fMRI data

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As I mentioned yesterday, there is a tendency when reviewing the output of a volume registration ("motion correction") algorithm to attribute all variations to real head motion. But, as was demonstrated last October, the magnetic susceptibility of the chest during breathing produces shifts in the magnetic field that vary spatially across the head, producing translations and shearing in EPI data that the volume registration algorithm can't distinguish from real head motion. Here I want to quickly review other major mechanisms by which we can get apparent head motion.

Let's start with contributions to real head motion. These include slow compression of foam designed to restrain the head, relaxation or tension of neck muscles, swallowing, fidgeting and the like. Printed head cases, bite bars and other restraint systems are of use here. Then there are body motions, including the extremities, that produce movement of the head via the neck. This is why you should instruct your subjects not to move at all during the scan. Telling a subject he shouldn't move his head is tantamount to saying that moving his feet is okay, and it's not. Subjects should move, e.g. to scratch or stretch, only when the scanner is silent.

Also included in the mechanical motion category is respiratory chest motion that couples unavoidably to the head because of that pesky neck thing. Pulsations of the brain with the cardiac cycle are another source of unavoidable direct motion in the organ of interest. The latter is real brain motion, of course.

Next, body motions (including from respiration) can produce head movement in the magnetic field via instability of the patient bed. Back in the early 2000s we had a Varian 4 T scanner. We had to construct rollers to catch and support the bed sled in the magnet bore because we had a cantilevered bed that deflected like a springboard otherwise. Every tiny movement of the subject caused the bed sled to bounce. For stability we want a strongly coupled system - subject to bed, bed to gradients/magnet - and we need to avoid any relative movement between them. I was reminded of this mechanism again recently. It's something to keep in mind as we work on respiratory instabilities because I note that my Trio has a bed cantilevered on the magnet face whereas Prisma scanners have a bed supported on the floor in front of the magnet. The latter should be a lot more stable, provided the bed has a solid foundation underneath it.

So far all the mechanisms I've considered have had a direct mechanical connection between the source of the motion and the brain. Chest motion can also affect the magnetic field via changing magnetic susceptibility from the air-filled lungs, as previously demonstrated. This is a through-space mechanism. In principle, movement of the extremities or any other part of the body (or other equipment in the bore) might also produce perturbation of the magnetic field across the head via magnetic susceptibility, but my intuition is that this would be a minor contributor to overall instability compared to the effects from the chest.

A well-known motion-like effect arises from thermal drift in the magnet. The gradients get warm with use and over time this causes drift in the magnetic field, e.g. via passive shimming iron that doesn't have the water cooling of the gradient set. Re-shimming can offset some of the effects of this mechanism between runs, but not within a run. When viewed from the perspective of your agnostic volume realignment algorithm, thermal drifts appear a lot like slow (real) head movements, e.g. as foam compresses or neck muscles relax. Re-shimming between runs helps with both, but I'm afraid it doesn't do anything within a run. De-trending is usually used to good effect here.

There are doubtless other sources of instability that can manifest as apparent head motion - anything that causes shifts in the on-resonance frequency during an EPI time series will do it - but here I've covered the main mechanisms of concern. Given robust head restraint to mitigate most of the direct head motion mechanisms (except brain pulsations), it seems that the next largest instabilities to tackle are the respiratory motion mechanisms. We have three to work on: residual direct motion through the neck, magnetic susceptibility of the chest, and the possible deflection of the patient bed.


Fluctuations and biases in fMRI data

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In my last post I summarized the main routes by which different forms of actual or apparent motion can influence fMRI data. In the next few posts, I want to dig a little deeper into non-neural causes of variation in fMRI data. I am particularly interested in capturing information on the state of the subject at the time of the fMRI experiment. What else can be measured, and why might we consider measuring it? Brains don't float in free space. They have these clever life support systems called bodies. While most neuroimagers reluctantly accept that these body things are useful for providing glucose and oxygen to the brain via the blood, bodies can also produce misleading signatures in fMRI data. My objective in this series of posts is to investigate the main mechanisms giving rise to fluctuations and biases in fMRI data, then consider ways other independent measurements might inform the fMRI results.

Many causes, much complexity

There are three broad categories of fluctuations or biases imprinted in the fMRI data. I've tried to depict them in Figure 1. At top-right, in a cartoon red blood vessel, is the cascade of physiological events leading to BOLD contrast. Next, on the left, there are perturbations arising from the subject's body. Some of these are direct effects, like head motion, and some are propagated via modulation of the same physiological parameters that give rise to BOLD. Breathing is a good example of the latter. A change in breathing depth or frequency can change the arterial concentration of CO2, leading to non-neural BOLD changes. Furthermore, the breathing rate is intricately tied to the heart rate, via the vagus nerve, and so we can also expect altered brain pulsation. In the final category, depicted in my figure as scanner-based mechanisms at the bottom, we have experimental imperfections. In the last group are things that could be reduced or eliminated in principle, such as thermal drift in the gradients, wobbly patient beds, and resonance frequency shifts across the head arising from changing magnetic susceptibility of the chest during breathing. The thin blue lines connecting the different parts of the figure are supposed to show the main influences, with arrowheads to illustrate the directionality.

(Click image to enlarge.)

Figure 1. Major routes of modulation in time series data in an fMRI experiment. The flow chart in the depiction of a blood vessel, in red, is based on a figure from Krainik et al. 2013 and shows the main events leading to BOLD via neurovascular coupling. Main body-based mechanisms originate on the left, and scanner-based experimental imperfections are depicted on the bottom. All mechanisms ultimately feed into the fMRI data, depicted at center. Yellow boxes contain some of the main modulators of mechanisms that can produce either fluctuations or systematic biases in fMRI data.

Abbreviations: ANS - autonomic nervous system, HR - heart rate, CBVa - arterial cerebral blood volume, CBVv - venous cerebral blood volume, CMRO2 - cerebral metabolic rate of oxygen utilization, CBF - cerebral blood flow, OEF - oxygen extraction fraction, deoxyHb - deoxyhemoglobin, AR - autoregulation, pO2 - partial pressure of oxygen (O2 tension), pCO2 - partial pressure of carbon dioxide (CO2 tension).


As if that wasn't already a lot of complexity, I'm afraid there's more. In the yellow boxes of Figure 1 are some of the main modulators of the underlying mechanisms responsible for perturbing fMRI data. These modulators are usually considered to be confounds to the main experimental objective. I posted a list of them a few years ago. Caffeine is probably the best known. It modulates both the arterial cerebral blood volume (CBVa) as well as the heart rate (HR). We already saw that HR and breathing are coupled, so this produces a third possible mechanism for caffeine to affect fMRI data. There's also an obvious missing mechanism: its neural effects. Some direct neural modulators are summarized in Figure 2, placed in their own figure simply to make this a tractable project. I'll be going back to reconsider any direct neural effects at the end of the series, to make sure I've not skipped anything useful, but my main emphasis is the contents of Figure 1.

Figure 2. Potential modulators of neural activity during an fMRI experiment.



Measuring the modulators

There are about a dozen mechanisms leading to fluctuations in fMRI data. Note that some paths depicted in Figure 1 may contain multiple discrete mechanisms. The figure would be far too cluttered if every mechanism was depicted. Take head motion. It could be foam compressing through no fault of the subject, or it could be the subject fidgeting, or apparent head motion arising from the sensitivity of the EPI acquisition to off-resonance effects (for which there are at least two main contributions: thermal drift in the scanner and chest motion in the subject). I tried to estimate how many combinations are represented in Figure 1 but quickly gave up. It's several dozen. I'm not sure that knowing the number helps us. Clearly, it's an omelette.

So, what can we do about it? Well, there are only so many things one can measure before, during or after an MRI scan, so we should probably start there. In the first set of posts in this series I'll look at non-MRI measures that can be performed during fMRI data acquisition, to track moment to moment changes in some of the parameters of Figure 1. These will include:
  • Heart rate
  • Blood pressure
  • Vascular low frequency oscillations in the periphery
  • Respiration rate
  • Expired CO2
  • Electrodermal activity
  • Eye tracking
  • Head motion

Then, in the next set of posts I'll shift to assessing ancillary MRI measurements that can inform an fMRI experiment, such as:
  • Anatomical scans
  • Baseline CBF
  • Blood oxygenation
  • Cerebrovascular reactivity
  • Calibrated fMRI (which is actually a slightly different way of doing the fMRI experiment, but requires some ancillary steps)

Finally, I'll consider informative, non-MRI data you could capture from questionnaires or relatively simple non-invasive testing. With better understanding, I am hoping that more researchers begin to consider physiology as earnestly as they do the domains involving psychology and statistics.


FMRI data modulators 1: Heart rate

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It's 2027 and you are preparing to run a new fMRI experiment. Since 2023 you've been working on a custom 7 T scanner that was developed to mitigate several issues which plagued the early decades of fMRI. Long gone are the thermal shim and gradient drifts of yesteryear, courtesy of an intelligent water cooling system that maintains all hardware at near constant temperature even when the scanner is run flat out. Your scanner also has a custom gradient set with active shielding over the subject's chest. It means the rise time of the gradients is limited only by peripheral nerve stimulation in the subject's face and scalp, not by the possibility of causing fibrillation in the heart. You can use a slew rate four times faster than on the scanner you had back in 2017, meaning distortions of your 1 mm cubic voxels, acquired over the entire brain (including cerebellum!) are minuscule. What's more, your images no longer suffer from translations and shearing because of the subject's chest motion. Your scanner tracks the magnetic field across the subject's head and actively compensates for the effects of breathing. When used with the comfortable head restraint system that mates directly to the receiver electronics - which itself monitors changes in coil loading to ensure the 128-channel array coil doesn't impart its own bias field onto your images - you have finally got to the point in your career where you no longer worry about head motion.

Almost. There's no doubt the hardware of the future could be remarkable compared to today's scanners. Our current scanners are clinical products being used for science rather than scientific instruments per se. However, even if we were to supersede BOLD with a non-vascular "neural current" contrast mechanism, the basic physics of MRI suggests that we will have to consider real brain motion in the future, just as we do today. Perhaps we can differentiate this brain motion from the contrast of interest using multiple echoes or some other trick, but I don't envisage being able to ignore the brain's vasculature entirely, whereas I am optimistic that improved scanner engineering might one day ameliorate the mechanical and thermal instabilities. Real brain motion and regional variation in pulsatility are likely to be biological limits that must be accommodated rather than eliminated.


What are the mechanisms of concern?

We can restrain the subject's skull quite well using a bite bar or a printed case. Inside the skull, however, is a gelatinous blob of brain, highly vascularized, under a small positive pressure (the intracranial pressure, ICP). The brain will tend to throb with the heart rate (HR) as blood is pumped into the brain through the arteries. The arterial network is spatially heterogeneous and so we see heterogeneous motion across the brain. The arteries enter at the base of the brain, causing the entire midbrain and brainstem to move relative to the cortex. Locally, tissue close to large vessels can demonstrate greater displacements than tissue just a a few millimeters away. These regional perturbations will arise with a range of delays relative to the cardiac output, as the blood pressure wave migrates from the heart. The greater the distance from the heart, the longer the lag. We'll see in a later post how this phenomenon can be used to estimate blood pressure.

There are also cardiac driven pulsations in the cerebrospinal fluid (CSF). These can be visualized as small displacements of tissue adjacent to the ventricular system as well as in sulci of the cortex. Pulsation in CSF and the changing velocity of blood in large vessels also tend to produce image contrast changes. This isn't real brain motion, of course, but it is a consideration if one is attempting to use local signal properties or overall image contrast to ameliorate regional pulsatility. A new paper by Viessmann et al. provides a timely investigation of the issues, concluding that fluctuations in partial volumes of blood and CSF/interstitial fluid give rise to local T2* changes over the cardiac cycle. So the final complexity is again temporal. The cardiac cycle is itself non-stationary, leading to dynamic changes in the locations of blood, CSF and brain tissue.


How is heart rate measured inside the scanner?

Outside the MRI environment it is possible to obtain detailed information on cardiac function through the electrocardiogram (ECG). Inside the MRI, the typical ECG response shape is significantly altered by magnetohydrodynamic and cardioballistic (or Hall) effects. (These effects also cause a significant source of artifacts in EEG recorded inside an MRI.) ECG also requires electrodes be placed on the chest, adding extra setup complications and privacy issues. Breasts and body fat can make it very difficult to get a good ECG signal from many subjects.

A convenient in-scanner measure of HR can be obtained from a photoplethysmograph, more commonly referred to as a pulse oximeter, albeit with less precision than when using the ECG outside the MRI. The signal processing used in pulse oximetry varies with the manufacture. Typically, the signal is filtered to optimize the instantaneous HR plus the (arterial) oxygenated hemoglobin fraction of total hemoglobin, termed SpO2. A detailed comparison found that pulse oximetry correlated strongly with heart rate variability (HRV) measured using ECG and we may thus consider oximetry an acceptable option for HR monitoring during fMRI.

While simple to use, pulse oximetry does have limitations. Motion of the sensor can be a problem, leading to erratic traces and the possibility that the signal is lost entirely. The sensor should be secured properly and subjects instructed on what not to move in order to maintain good data. Most often a finger is used for oximetry but if a study requires bimanual responses then a toe might be considered. Note, however, that certain subjects with low peripheral circulation can be hard to record from. The scanner suite temperature can be a major factor; consider subject comfort and warmth.


When might heart rate vary?

Numerous factors can alter HR. Recent exercise is an obvious one. Even at rest, however, the instantaneous HR is a consequence of complex interactions between the sympathetic and parasympathetic nervous systems, together referred to as the autonomic nervous system. For example, a degree of arrhythmia (usually referred to as the respiratory sinus arrhythmia, RSA) is a natural fluctuation of HR produced during the normal breathing cycle. Instantaneous HR increases slightly during inspiration and decreases slightly during expiration. The RSA produces modulation of around 0.15-0.4 Hz on top of typical resting heart rates in the range 0.5-1.5 Hz. A slower modulation, typically 0.04-0.15 Hz, may also occur. The precise mechanisms generating the slow modulation are less well understood but are generally considered to involve changes in arterial tone, and/or cerebral autoregulation to maintain a constant cerebral blood flow in spite of changes in overall blood pressure. I will be doing a separate post on these vascular low frequency oscillations; they can be detected in the periphery with suitable modifications to the pulse oximetry.

Cardiac output is also affected by arousal. It is is common to find components of HRV used as a measure of autonomic activity, e.g. anxiety, in psychology experiments, but given the broad spectrum of potential influences on HRV it is obviously important to apply rigorous control to extraneous factors, including exercise, pharmaceutical and other compounds including caffeine and alcohol, and some disease states, particularly diseases affecting the vasculature.


Using heart rate data

The HR is generally rapid compared to a typical fMRI sampling rate of 0.5 Hz for TR = 2000 ms. In this case the effects of HR will be aliased, making it easy to mistake cardiac for low frequency neurovascular fluctuations, or a task effect. For task-based fMRI, a convenient tactic is to ensure experimental power is placed well away from aliased cardiac (and respiratory) frequencies. This is usually assumed to be sufficient, especially if physiological noise regressors are used in the analysis. The situation is more complicated in resting-state fMRI because there is no external driving function against which to evaluate brain activity.

The issue of HRV as a potential confound in resting-state fMRI data was first addressed by Shmueli et al. in 2007 using cross-correlation of the cardiac waveform with the fMRI data, allowing for different delays between the two data sets. The generality of HRV analysis was extended by Chang, Cunningham & Glover (2009) using the concept of a canonical cardiac response function (CRF) convolved with the HR time series data, by analogy with the hemodynamic response function (HRF) used in event-related fMRI analyses. Using this analysis method, Chang and colleagues were able to delineate transient changes of autonomic nervous system states manifest in brain network connectivity during rest, suggesting that the specificity of their method is sufficient to discriminate confounding signal changes when arousal may not be under experimental control. More recent work by Falahpour et al. explored the utility of subject-specific CRF, while very recently de la Cruz et al. suggested that it might be better to separate subjects into groups based on HR, and use a separate mean group CRF for low (48-68 bpm) and high (68-96 bpm) heart rates. The differing explanatory power seems to be related to slight differences in the dynamics of HR variation, raising the possibility that subjects with higher HR may be more highly aroused, perhaps because of greater scanner anxiety. Alternatively, the HR grouping might be a consequence of underlying cardiovascular health, or differing starting conditions such as recent exercise or caffeine use. These findings are a timely warning that even when attempting to remove HR effects from resting fMRI data, group-wise differences in HR could lead to significant residual effects dependent on mean HR.

There are now several comprehensive reviews that consider cardiac "nuisance signals" and "data cleaning" or "de-noising," especially for resting-state fMRI where physiological confounds are of great concern. If you are interested in applying such methods then I strongly urge you to read all the reviews and then the primary references before doing anything. I suggest you start with the excellent review by Caballero-Gaudes & Reynolds. If you're not already convinced of the complications, this paper should get you over that particular hump. As yet, there is no consensus on a best approach to dealing with nuisance signals. One reason for this is prosaic: different studies investigating physiological signals have different independent data to utilize. Some consider HR alone, some consider HR plus one or more further independent traces, such as chest motion and expired CO2. What you do depends on what you've got available to you. Then there is the vast parameter space to consider, with TR, voxel size, echo train length and many other parameters likely to contribute to the relative efficacy of one "nuisance signal" reduction method over another for a particular application. And finally there are statistical implications, as Caballero-Gaudes & Reynolds highlight:
"...similar to other approaches based on nuisance regression, adding more physiological noise regressors does not necessarily lead to improvement in BOLD sensitivity and higher statistical significance due to the loss in degrees of freedoms and possible correlations of the physiological regressors with the BOLD fluctuations generated by the experimental paradigm in task-based fMRI or the intrinsic neuronal fluctuations in the resting state. Hence, the optimal set of regressors will depend on the sequence and parameters of acquisition, as well as the regions of interest."


Final thoughts

Until someone proves otherwise, I advocate acquiring a separate pulse oximetry signal for all resting state fMRI scans, and it is likely prudent for all task fMRI experiments. Even if you can address your own questions without resorting to physiological data, having independent physiological measures available may make subsequent use of data by others more powerful.

FMRI data modulators 2: Blood pressure

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If you conduct fMRI experiments then you'll have at least a basic understanding of the cascade of events that we term neurovascular coupling. When the neuronal firing rate increases in a patch of brain tissue, there is a transient, local increase of the cerebral blood flow (CBF). The oxygen utilization remains about the same, however. This produces a mismatch in the rate of oxygen delivered compared to the rate of oxygen consumption. The CBF goes up a lot while the oxygenation usage increases only slightly. Hence, there is a decrease in the concentration of deoxygenated hemoglobin in the veins draining the neural tissue region, in turn reducing the degree of paramagnetism of these veins that yields a signal increase in a T2*-weighted image. The essential point is that it's blood delivery - changes in CBF - that provides the main impetus for BOLD contrast.


How is blood pressure related to CBF?

The average CBF in a normal adult brain is typically maintained at around 50 ml of blood per 100 g of brain tissue per minute (50 ml/100g/min). The average number, while useful, represents considerable spatial and temporal heterogeneity across the brain. The typical CBF in gray matter is approximately double that in white matter, and there is significant variation across each tissue type arising from tight metabolic coupling. (See Note 1.)

At the local level, blood delivery to tissue is controlled by smooth muscles on the walls of arterioles and capillaries. The degree of vessel dilation, relative to that vessel's maximum possible dilation, is called its tone - the vascular tone. There are mechanisms to expand or constrict the smooth muscles, changing the local blood flow in order to maintain the tight local coupling of CBF to metabolic demand while protecting the vasculature and the tissue against damage that might arise with systemic changes in the blood supply from non-neural mechanisms. The totality of these processes is referred to as cerebral autoregulation. More on the non-neural factors later.

This is all very well, but there is something important missing from this picture. We have neglected to consider so far that the force of blood pumped out of the heart creates a pressure gradient across the arteries and the veins, with the tissue providing a resistance in between. It's this pressure gradient that causes the blood to flow. In fact, simple electrical circuits are a convenient model here. For those of you more familiar with electron flow than blood flow, we can think of the CBF as an analog of electrical current, the pressure difference as a voltage and, naturally enough, the tissue's resistance to flow mimics an electrical resistance. Thus we get:

CBF = CPP / CVR

where CPP is the cerebral perfusion pressure, the net pressure gradient - the driving force - that generates perfusion of brain tissue, and CVR is the cerebrovascular resistance. The CVR is the sum total of all mechanisms exerting control over the vascular tone at a particular location. It isn't easily estimated without detailed knowledge of the processes that might be active. The neurovascular coupling pathways contribute to CVR, for example.

The CPP is more easily estimated. It is defined as the difference between the mean arterial blood pressure (MABP) and either the venous or intracranial pressure (ICP), whichever is lower. A typical ICP is 7-12 mmHg above the ambient (local atmospheric) pressure that is assumed to be 0 mmHg. In other words, the brain is under a small positive pressure that pushes against the skull. We also see that because MABP is quite a lot higher than ICP, there is a very close relationship between CBF, which is our parameter of relevance to BOLD contrast, and the MABP. Under normotensive conditions we can use MABP as a rough estimate of CPP, to give:

CBF ~ MABP/CVR

We have essentially averaged over the cardiac cycle here, and reduced the control of the CBF to one global (systemic) parameter - the MABP - that is regulated locally via CVR. So now we need a convenient way to assess the MABP.

Before we do that, though, let's first get familiar with the blood pressure nomenclature you've almost certainly encountered when you go to see your doctor. "One fifteen over seventy five" is not, in fact, a cricket score. Here are some quotes from the Wikipedia entry on blood pressure:
"Blood pressure (BP) is the pressure of circulating blood on the walls of blood vessels. When used without further specification, "blood pressure" usually refers to the pressure in large arteries of the systemic circulation. Blood pressure is usually expressed in terms of the systolic pressure (maximum during one heart beat) over diastolic pressure (minimum in between two heart beats) and is measured in millimeters of mercury (mmHg), above the surrounding atmospheric pressure (considered to be zero for convenience).
For each heartbeat, blood pressure varies between systolic and diastolic pressures. Systolic pressure is peak pressure in the arteries, which occurs near the end of the cardiac cycle when the (cardiac) ventricles are contracting. Diastolic pressure is minimum pressure in the arteries, which occurs near the beginning of the cardiac cycle when the ventricles are filled (filling would be better) with blood. An example of normal measured values for a resting, healthy adult human is 120 mmHg systolic and 80 mmHg diastolic (written as 120/80 mmHg, and spoken as "one-twenty over eighty")."

With an understanding of the maximum (systolic) and minimum (diastolic) BP values in our kitbag we can go back to the idea of a mean arterial BP. The MABP is the temporal average blood pressure over the cardiac cycle. For normal resting heart rate, a convenient estimate of MABP can be derived from the systolic (SP) and diastolic pressures (DP) as:

MABP  ~  DP + (SP - DP)/3 .

The MABP is considered to be the perfusion pressure experienced by organs throughout the body, including the brain. The difference, SP - DP, is termed the pulse pressure and is one of the parameters susceptible to change in certain disease conditions and aging. From Wikipedia again:
"Pulse pressure is determined by the interaction of the stroke volume of the heart, the compliance (ability to expand) of the arterial system—largely attributable to the aorta and large elastic arteries—and the resistance to flow in the arterial tree. By expanding under pressure, the aorta absorbs some of the force of the blood surge from the heart during a heartbeat. In this way, the pulse pressure is reduced from what it would be if the aorta were not compliant. The loss of arterial compliance that occurs with aging explains the elevated pulse pressures found in elderly patients."


What's the concern for fMRI?

Reconsider the relation CBF ~ MABP/CVR. Brain tissues have regional control over CVR to ensure the CBF satisfies local metabolic demands on the one hand, while on the other hand autoregulatory processes assure no local over pressure that might lead to hemorrhage. Small moment to moment changes in MABP can be accommodated by the autoregulatory processes to ensure the CBF is maintained at the rate required by local energy considerations. But how much variation in MABP can the autoregulatory compensating mechanisms handle? And what happens if MABP is abnormally high or low for a prolonged period of time, as might be the case with some disease states? Any systematic differences in MABP between groups, between conditions or over time might drive alterations in CBF, and consequently BOLD, that are interpreted as having a neural basis when they are actually caused by systemic blood pressure effects. Thus, we can recast our question of concern as: "When does MABP vary, and by how much?" This should give us a good starting point for assessing the potential contribution of BP variation to an fMRI study.

Let's take a look at "normal autoregulation."From Wikipedia again:
"Under normal circumstances a MAP between 60 to 160 mmHg and ICP about 10 mmHg (CPP of 50-150 mmHg) sufficient blood flow can be maintained with autoregulation.[1][2] Although the classic 'autoregulation curve' suggests that CBF is fully stable between these blood pressure values (known also as the limits of autoregulation), CBF may vary as much as 10% below and above its average within this range.[3]

Outside of the limits of autoregulation, raising MAP raises CPP and raising ICP lowers it (this is one reason that increasing ICP in traumatic brain injury is potentially deadly). In trauma some recommend CPP not go below 70 mmHg.[4][5] Recommendations in children is at least 60 mmHg.[4]

Within the autoregulatory range, as CPP falls there is, within seconds, vasodilatation of the cerebral resistance vessels, a fall in cerebrovascular resistance and a rise in cerebral blood volume (CBV), and therefore CBF will return to baseline value within seconds (see as ref. Aaslid, Lindegaard, Sorteberg, and Nornes 1989: http://stroke.ahajournals.org/cgi/reprint/20/1/45.pdf). These adaptations to rapid changes in blood pressure (in contrast with changes that occur over periods of hours or days) are known as dynamic cerebral autoregulation.[3]"

Variations of as much as 10% from non-neural factors are going to compete handily with BOLD signal changes produced by neurovascular coupling. In normal, healthy volunteers we are primarily concerned about the dynamics of autoregulation in response to acute changes in MABP, and responses "within seconds" sound like the time scale for fMRI experiments.

The potential for BP variation to confound BOLD signal changes to a stimulus was nicely demonstrated by Wang et al. They induced transient hypertension and hypotension in rats with pharmaceuticals and investigated the relationship between forepaw stimulation and BP, finding:
"During transient hypertension, irrespective of forepaw stimulation, BP increases (i.e., >10 mm Hg) produced a transient increase in the blood oxygen level-dependent (BOLD) intensity resulting in a significant numbers of voxels correlating to the BP time courses (P < 0.05), and the number of these voxels increased as BP increased, becoming substantial at BP > 30 mm Hg. The activation patterns with BP increases and stimulation overlapped spatially resulting in an enhanced cerebral activation to simultaneous forepaw stimulation (P < 0.05). BP decreases (>10 mm Hg) produced corresponding decreases in BOLD intensity, causing significant numbers of voxels correlating to the BP decreases (P < 0.005), and these numbers increased as BP decreased (P < 0.001)."

A study by Lui et al. in cocaine-dependent human subjects found that dobutamine infusion raised MABP but produced only localized BOLD signal changes in anterior cingulate that correlated with the BP rise. However, their study didn't employ a task, leaving open the possibility of interactions between tasks and BP changes.

What about humans not on drugs? Lots of perfectly normal, everyday things affect our BP. There are circadian changes, with greater BP in the morning and evening and lowest BP during sleep. Blood pressure and CBF change during and immediately after exercise, as demonstrated by Macintosh et al. and Smith et al. 

Abnormal BP is also of concern for patients with likely impairment of cerebral autoregulation, including traumatic brain injury (TBI), hypertension, hypotension (including major blood loss, perhaps including very recent blood donation) and neurodegenerative conditions. For example, Alzheimer’s patients studied with transcranial Doppler ultrasound exhibited a low frequency variability in BP suggestive of impaired homeostasis.

The broad range of situations in which BP may change, and the strong relationship between MABP and CBF, suggests that caution is warranted. It is conceivable that variations in BP could be as consequential as respiration rate (more specifically, arterial CO2 concentration) or caffeine consumption in causing BOLD signal instability across groups of otherwise similar people, or across time for individuals. And, of course, BP fluctuations could be especially important in tasks where changes in BP might be strongly correlated with certain classes of stimuli.


Using BP data in fMRI experiments

Taking a blood pressure measurement before or after a scan may be informative but it's also insufficient. Baseline BP (before MRI) was found by Lu, Yezhuvath & Xiao to offer only a small normalizing effect on visual-evoked BOLD signals when tested across two conditions, whereas other physiological parameters had considerably more explanatory power.

Gianaros et al. observed a correlation between MABP and BOLD activity in several brain regions of participants conducting a stressful Stroop task, with BP measured once for each block of sixteen 90-second task blocks. In a later study with BP measured in the scanner once a minute, the same task produced a correlation between stressor-evoked MABP reactivity and amygdala activation. 

If one has a time series of BP data then one can consider "de-noising" methods, such as regressing BP from the signal. Murphy et al. used partially inflated pressure cuffs (more on this below) to record BP once per heart beat. The BP explained 3-14% of the variance in global BOLD signal, which is about the same as is generally explained by more common physiological recordings. For example, Golestani et al. recently showed that cardiac and respiratory variability measures plus expired CO2 accounted for 5-24% of BOLD signal variability, depending on the subject. What's most notable in Murphy's BP study is the optimal lag, which was less than the repetition rate (TR) of 3 seconds. They suggest that the influence of BP on BOLD signal should be near instantaneous if it reflects CBF fluctuations subject to cerebral autoregulation.


How is BP measured non-invasively?

The familiar blood pressure measurement is performed on the brachial artery of your upper arm and uses a device called a sphygmomanometer. A what? My thoughts exactly. This is the only time I'll ever use the term since I can't pronounce it. (And if you insist on using unpronounceable medical terms to sound intelligent, in return I shall insist that you refer to MRI as zeugmatography, so there.) In Note 2, below, you'll find an explanation of how BP is measured in your doctor's office using the device with the unnecessarily fancy name. We don't need to get into its details because the standard method gives a single BP value whereas for fMRI - sorry, functional zeugmatographic - experiments we want a method that can give continuous, simultaneous BP sampling of the subject inside the scanner. At a minimum we want one BP value per heart beat.

There are commercial devices that will measure BP inside an MRI but they don't satisfy our criterion of a sample per heart beat. These devices use similar principles as the fancy word method, except that electronic circuits replace the human listening for the blood sounds in your arm. They are referred to as oscillometric BP measures. The requirement to inflate a cuff and monitor its release means that these methods take tens of seconds to get a single measurement. It is also uncomfortable and likely distracting for fMRI applications.

It turns out to be quite difficult to perform continuous non-invasive blood pressure monitoring (NIBP) at all, let alone on a subject in an MRI scanner. Discomfort, motion sensitivity and highly accurate placement of sensors relative to arteries all contribute to a general lack of robustness for many applications. There have been several attempts, however, and we can loosely divide the approaches into three groups: volume clamps (also known as vascular unloading methods), pulse wave velocity recordings, and pulse decomposition analysis. I'll review all three in a bit of detail because it could be instructive for labs attempting custom solutions, and provide guidance on what to look for if ever you go shopping for a commercial device.

Volume clamp:  A volume clamp, such as the commercially availablePortapres device from Finapres Medical Systems, comprises an optical source and a sensor attached to a finger, like a standard pulse oximeter except that the device also includes a small cuff which changes the pressure applied to the finger. With conventional pulse oximetry we measure the blood volume in the tissue from heartbeat to heartbeat. In the volume clamp method a small pressure is applied to the finger via the cuff, essentially clamping the arterial blood at a constant volume. Now, as the pressure wave arrives from the heart, the finger's arteries regulate their local pressure to maintain constant blood flow and avoid rupturing. Yup, local autoregulation again! A sensor recording the pressure in the cuff now reports changes in the beat to beat blood pressure of the finger, as shown in the figure below. The volume clamp is a relative measure and requires calibration to get absolute BP, but the bigger issue, apparently, is the extreme motion sensitivity.

Fig. 4 from Peters et al. 2014: https://doi.org/10.1016/j.irbm.2014.07.002. The principle of the volume clamp method is based on a combination of standard pulse oximetry (photoplethysmography) with a pressure cuff on a finger. With the cuff uninflated the pulse oximeter reports the beat to beat blood volume (left side). With the cuff inflated the blood volume is clamped, eliminating the signal in the pulse oximeter (right side, lower trace). However, a manometer recording pressure in the cuff now reports changing blood pressure in the finger (right side, upper trace).


Pulse wave velocity:  The second class of NIBP monitors involve measuring the time taken for the systolic pressure wave to travel from the left ventricle of the heart to other locations in the body. Every time the heart contracts, ejecting blood into the aorta, it produces a pressure wave that propagates throughout the entire arterial system. (Note that the pressure wave travels faster than the blood flow. You might think of it like a sound pressure wave being carried in the wind. Sound travels faster than the air is moving.) The time taken for the pressure wave to travel to a point is called the pulse transit time (PTT). The pulse wave velocity (PWV) may then be determined using two BP sensors placed a known (arterial) distance d apart, as PWV = d/PTT. The PTT, hence PWV, depends upon systemic blood pressure via characteristics of the vascular system: the elasticity and thickness of the arterial walls, the end-diastolic arterial diameter, and blood density. As we have already seen, as systemic BP increases there are autoregulatory processes to ensure increases in arterial diameter and compliance (the reciprocal of elasticity) to maintain constant blood flow to organs and avoid hyperperfusion. Thus, an increased systemic BP produces decreased PTT and increased PWV.

All that sounds rather complicated. And if you look up articles on PWV you will find that it is. But we don't need to get that deeply involved in elasticity and whatnot, because a relative BP measure will suffice. We want a plot of changes in BP over time rather than absolute quantification, as would be important in a medical scenario. For our purposes, then, all we need is two sensors a different arterial distance from the heart, and to determine the difference in the arrival times of the pressure waves. For fixed sensor placement, any changes in BP will modulate the difference in arrival times for the pressure pulse and give us our time course. Consider the setup illustrated in this figure from Murphy, Birn & Bandettini:


In their setup, one pressure cuff is placed on a bicep at the same level as the heart, while a second cuff is placed on a thigh a distance D away. Optical sensors could be used instead of pressure cuffs, but these still produce one BP estimate per heart beat. In a custom device built specifically for MRI compatibility, one optical sensor was placed directly over the aortic valve on the sternum and the second over a carotid artery. In my lab we're tinkering with PTT approaches right now, trying to determine if we can get robust signals out of the same pressure pads we use for monitoring chest motion. Early tests are encouraging, but we're not yet ready to spend money on all the parts we'd need let alone put it into routine use! As soon as there's something definitive to say, count on a blog post on it.

Pulse decomposition analysis: The PWV methods use two sensors to measure differential arrival times of the same pressure wave. With pulse decomposition analysis (PDA) it's the reverse. The goal is to use a single sensor and measure differential timing information from two (or more) reflected pressure waves. Let's jump right in and look at the anatomical origins of these reflected waves, then we can look at the analysis and methodological limitations. Here's a schematic of the main pressure wave, labeled P1, and two reflected waves, P2 and P3, that are produced at the levels of the renal and iliac arteries, respectively:

Figure 1 from Baruch et al. 2011. The main arterial tree is depicted on the right. It shows the initial pressure wave, #1, created by blood ejected from the heart, descending from the aortic arch. This wave also travels down the brachial artery, where it is depicted arriving at the radial artery as signal P1. The main pressure wave reflects at the juncture of the thoracic and abdominal aorta, at the level of the renal arteries, and also at the juncture of the abdominal aorta and the common iliac arteries, producing reflected signals P2 and P3 that travel back up and are eventually detected in the radial artery at times T12 and T13, respectively.

The sensor is on a finger, at the distal end of the radial artery. The signal sensed at the finger is depicted on the left of the figure above. The sensor detects the main pressure wave, P1, after a relatively short, direct journey down the arteries of the arm. Reflected waves P2 and P3 have traveled farther: down to the level of the renal and iliac arteries, respectively, before traveling back up through the arterial tree, over into the radial artery and down to the finger, where they are detected. There are other reflected waves - reflections of reflections - but these are much weaker and we don't need to worry about them. Reflected pulse P2 arrives at time T12, typically 70-140 ms later than P1, while reflected pulse P3 arrives at time T13, 180-400 ms later.

The amplitude and timing of the primary and reflected pulses are then fed into the PDA model. How does the model estimate BP? According to a validation study performed by the method's inventors:
"The first reflection site is the juncture between thoracic and abdominal aorta, which is marked by a significant decrease in diameter and a significant change in elasticity. The reflection coefficient of this juncture is highly sensitive to blood pressure changes because of the pressure-dependent expansion of the diameter of the thoracic artery relative to that of the abdominal artery. The second (reflection) site arises from the juncture between abdominal aorta and the common iliac arteries. The renal site reflects the pressure pulse because the juncture of the aortic arteries there features significant changes in arterial diameter and wall elasticity."
The specific algorithm used in PDA is proprietary, but they do tell us the key parameters in a product manual. The amplitude ratio P2/P1 is used to track beat-to-beat systolic pressure:
"The physiological model here is that the reflection coefficient of the P2 reflection site is highly pressure dependent. The reason is due to the difference between the Young’s modulus of the thoracic aorta (the “softest” artery of the body) and the abdominal aorta. With increasing systolic pressure the thoracic aorta dilates more than abdominal aorta, resulting in an increasing diameter mismatch between the two aortic sections. Decreasing pressure has the opposite effect, as is easily demonstrated by performing the valsalva maneuver."
Then, the differential delay T13 between the arrival of P1 and reflected signal P3 is used to track changes in pulse pressure:
"The physiological model is that, since both pulses travel at different pressure amplitudes, they also travel at different pulse propagation velocities. As the differential pressure between them changes, so will their relative arrival time because their individual pulse propagation velocities change, causing them to accelerate or decelerate relative to each other."
Recall that pulse pressure is defined as (SP - DP), so now we can easily compute diastolic pressure from the pulse pressure and systolic pressure.


Continuous NIBP in the MRI scanner

So, three broad approaches. Which one do we use for routine fMRI? This is where reality bites, I'm afraid. Gray et al. modified their Portapres volume clamp to work in their 3 T scanner. So far, however, I've not found any details on the modifications they made. Murphy et al.and Myllylä et al. both used pulse wave velocity, with pressure cuffs and optical sensors, respectively, but both are also custom setups. Finally, Whittaker et al. (ISMRM abstract #0309, 2016) recently tested the pulse decomposition analysis method used in the commercial CareTaker device, obtained through BIOPAC, Inc.

I don't know about you, but as an MRI person I have a particular affinity for anything that echoes. The PDA approach is just so damned elegant. Even the nomenclature - T12, T13, P1, P2, etc. - sounds reassuringly familiar.  Except that we have a problem. The previous re-seller, BIOPAC, no longer offers the product. I did a bit of online sleuthing and it looks like CareTaker have gone on to bigger and better things. That is, they got FDA clearance, have given their product's packaging a cuddly facelift and are all set to sell thousands of devices for medical use. The small fMRI research market is probably not on their radar any longer. (I don't blame them. And I wish them continued good luck!) Perhaps we can still get CareTaker devices for research purposes. Other than the packaging it looks to be the same essential device as BIOPAC was re-selling. It may cost a lot more now, given FDA approval, and you may have to go through a medical equipment supply company to get one, but these are issues I've not broached yet.

The commercial Portapres device isn't compatible with MRI. You'd need to customize it. Pulse wave velocity might be easier to do in principle, but there's no recommended routine cuff-based method yet, and getting two cuffs on a subject, one on a thigh, may not be easy to do. For PWV with optical sensors we have two obstacles. Firstly, they were a custom development in a Finnish lab. Secondly, one optical sensor needs to be placed directly over the aorta, introducing huge privacy issues even if it works really well.

Given that commercial solutions are not yet guaranteed to work for us, I'm exploring custom approaches to PWV (strictly, PTT) as I mentioned above. We're testing pulse oximeter positions and we're testing pressure sensors. We already tried comparing pulse oximetry on a finger to a single pressure sensor on a femoral artery. The signals for both looked pretty good, except that there is no lag in the optical signal whereas the pressure signal has sufficiently long lag to render the time difference minuscule. And reversing the sensor placement isn't an option. We're now trying to devise robust configurations of two of the same types of sensor, to keep the lags consistent. In the mean time, if anyone purchases a new CareTaker device direct from the company, please let me know how much you paid for it and whether it's working well in your scanner. The Portapres device is still an option, of course, but I am concerned about motion sensitivity as well as overall sensitivity. Tasks that require the use of hands for response essentially rule out pulse oximetry, while my 17 C scanner suite can make it difficult to get good pulse oximetry from many subjects.


Final thoughts

There is tantalizing evidence and good theoretical reasons to think that a non-invasive blood pressure measurement would be informative and complimentary to the information available in the heart and respiration rates, and expired CO2. However, at the moment the equipment to do NIBP inside the MRI scanner needs more development and testing. I encourage those labs pursuing BP measurements to get more information out in public as soon as reasonably possible. If we can reach consensus on a methodology then we can figure out how to buy/build the solution and start on the path of routine NIBP measurement.

Next up in this series: Low frequency oscillations. What are they, and how do they relate to BP?

____________________


Acknowledgements

Many thanks to Molly Bright and Dan Handwerker for sending me several references and helping me understand the limitations of current NIBP methods.


Notes

1. It is generally assumed that the CMRO2 - the metabolic rate of oxygen utilization - is very tightly coupled to local metabolic demand. For the purposes of this post I am going to assume that CBF is also tightly coupled to metabolism. Perhaps the coupling isn't quite as tight between CBF and metabolic demand as CMRO2 and metabolic demand; this is a detail we don't need to worry about here. It is quite clear from PET and other studies that we can use blood delivery as a good proxy for cellular activity, loosely defined, on a timescale of seconds to tens of minutes.

2.  Measuring blood pressure with a cuff:

(Extracted from the Wikipedia page on the sphygmomanometer.)
A sphygmomanometer, also known as a blood pressure meter, blood pressure monitor, or blood pressure gauge, is a device used to measure blood pressure, composed of an inflatable cuff to collapse and then release the artery under the cuff in a controlled manner, and a mercury or mechanical manometer to measure the pressure. It is always used in conjunction with a means to determine at what pressure blood flow is just starting, and at what pressure it is unimpeded. Manual sphygmomanometers are used in conjunction with a stethoscope.

The cuff is normally placed smoothly and snugly around an upper arm, at roughly the same vertical height as the heart while the subject is seated with the arm supported. It is important that the cuff size is correct: undersized cuffs record too high a pressure, oversized cuffs may yield too low a pressure. Usually three or four cuff sizes should be available to allow measurements in arms of different size.

A stethoscope is generally required. Manual meters are used by trained practitioners. Listening with the stethoscope to the brachial artery at the antecubital area of the elbow, the examiner slowly releases the pressure in the cuff. As the pressure in the cuffs falls, a "whooshing" or pounding sound is heard (see Korotkoff sounds) when blood flow first starts again in the artery. The pressure at which this sound began is noted and recorded as the systolic blood pressure. The cuff pressure is further released until the sound can no longer be heard. This is recorded as the diastolic blood pressure.

Digital meters employ oscillometric measurements and electronic calculations. They may use manual or automatic inflation, but both types are electronic, easy to operate without training, and can be used in noisy environments. They measure systolic and diastolic pressures by oscillometric detection, employing either deformable membranes that are measured using differential capacitance, or differential piezoresistance, and they include a microprocessor.

Digital instruments use a cuff which may be placed, according to the instrument, around the upper arm, wrist, or a finger, in all cases elevated to the same height as the heart. They inflate the cuff and gradually reduce the pressure in the same way as a manual meter, and measure blood pressures by the oscillometric method. They accurately measure mean blood pressure and pulse rate, while systolic and diastolic pressures are obtained less accurately than with manual meters, and calibration is also a concern.


COBIDAcq?

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WARNING: this post contains sarcasm and some swearing.
(But only where absolutely necessary.)


COBIDAcq, pronounced "Koby-dack," is the Committee on Best Practice in Data Acquisition. It is based on the similarly dodgy acronym, COBIDAS: Committee on Best Practice in Data Analysis and Sharing. I suppose COBPIDAAS sounds like a medical procedure and CBPDAS is unpronounceable, so COBIDAS here we are.

Unlike COBIDAS, however, the COBIDAcq doesn't yet exist. Do we need it? The purpose of this post is to wheel out the idea and invite debate on the way we do business.


Why a new committee?

You know the old aphorism: "Act in haste, repent at leisure?" It's not just for US tax reform. We have a lot of errors made in haste in fMRI. You may have noticed. Some of the errors may be directly under an experimenter's local control, but many are distributed by influential people or through limitations in commercial products. Whatever the root causes, unless you think fMRI has already attained methods nirvana, there is ample reason to believe we could do a lot better than the status quo.

The COBIDAS approach is intended to "raise the standards of practice and reporting in neuroimaging using MRI," according to its abstract. I am still seeing weak evidence there has been wholesale adoption of the COBIDAS suggestions for reporting. (Feel free to pick up your latest favorite paper and score it against the COBIDAS report.) Thus, I'm not wholly convinced practice in neuroimaging will benefit as much as intended, except to help people disentangle what was done by others and avoid their mistakes at some much later stage, perhaps. What I'm after is intervention a lot earlier in the process.


Risks and systematic errors in an era of Big Data

A long time ago I wrote a post about taking risks in your experiment only if you could demonstrate to yourself they were essential to your primary goals. New is rarely improved without some harmful - often unknown - consequences. Rather, what new usually gets you is new failure modes, new bugs, a need to change approach etc. So if you have a really good idea for a neuroscience experiment and you can achieve it with established methods, why insist on using new methods when they may not help but may cause massive damage? That is tantamount to placing your secondary goals - impressing a reviewer with yer fancy kit - ahead of your primary goals. Crazy!

There is a lot of energy presently going into data sharing and statistical power. This is great n' all, but what if the vast data sets being cobbled together have systematic flaws; potentially many different systematic flaws? How would you know? There are some QA metrics that attempt to capture some of the obvious problems - head motion or gradient spiking - but do you trust that these same metrics are going to catch more subtle problems, like an inappropriate parameter setting or a buggy reconstruction pipeline?

I'd like to propose that we redirect some of this enthusiasm towards improving our methods before massively increasing our sample size to the population of a small market town. Otherwise we are in danger of measuring faster-than-light neutrinos with a busted clock. No amount of repeat measures will tell you your clock is busted. Rather, you need a sanity check and a second clock.

Here are some examples of common problems I see in neuroimaging:
-  Taking a tool that worked at one field strength and for one sort of acquisition and assuming it will work just as well at a different field strength or with a different acquisition, but with little or no explicit testing under the new circumstances.

-  New and improved hardware, sequences or code that are still in their honeymoon phase, foisted into general use before rigorous testing. Only years later do people find a coding bug, or realize that widely used parameters cause problems that can be avoided with relative ease.

-   Following others blindly. Following others is a great idea, as I shall suggest below, but you shouldn't assume they were paying full attention or were sufficiently expert to avoid a problem unless there is documented evidence to refer to. Maybe they got lucky and skirted an issue that you will run into.

And here's my final motivation. It's difficult enough for experienced people to determine when, and how, to use certain methods. Imagine if you were new to neuroimaging this year. Where on earth would you start? You might be easily beguiled by the shiny objects dangled in front of you. More teslas, more channels, shorter repetition times, higher spatial resolution.... If only we could use such simple measures to assess the likelihood of experimental catastrophe.


Ways to improve acquisition performance

I think there are three areas to focus on. Together they should identify, and permit resolution of, all but the most recalcitrant flaws in an acquisition.

1. Is it documented?

Without good documentation, most scientific software and devices are nigh on unusable. Good documentation educates experts as well as the inexperienced. But there's another role to consider: documenting for public consumption is one of the best ways yet devised for a developer to catch his errors. If you don't believe this to be true, you've never given a lecture or written a research paper! So, documentation should help developers catch problems very early, before they would have seen the light of day.

While we're talking documentation, black boxes are a bad idea in science. If it's a commercial product and the vendor doesn't tell us how it works, we need to open it up and figure it out. Otherwise we're conducting leaps of faith, not science.

2. How was it tested at the development stage?

Understandably, when scientists release a new method they want to present a good face to the world. It's their baby after all. When passing your creation to others to use, however, you need to inject a note of realism into your judgment and recognize that there is no perfectly beautiful creation. Test it a bit, see how it falls down. Assess how badly it hurts itself or things around it when it crashes through the metaphorical coffee table. Having done these tests, add a few explanatory notes and some test data to the documentation so that others can see where there might be holes still gaping, and so they can double-check the initial tests.

3. Has it been validated independently and thoroughly?

Today, the standard new methods pipeline can be represented in this highly detailed flow chart:

Developer  →  End user

Not so much a pipeline as quantum entanglement. This is a reeeeeally bad idea. It makes the end user the beta tester, independent tester and customer all in one. Like, when you're trying to complete a form online and you get one of those shibboleth messages, and you're like "What. The. Fuck! Did nobody bother to test this fucking form with Firefox on a Mac? Whaddayamean this site works best with Internet Explorer? I don't even own a PC, morons! How about you pay a high school student to test your fucking site before releasing it on the world?"

Okay, so when this happens I might not be quite that angry... Errr. Let's move on. After better documentation, independent validation is the single biggest area I think we need to see improvement in. And no, publishing a study with the new method does not count as validation. Generally, in science you are trying your hardest to get things to work properly, whereas during validation you are looking to see where and how things fail. There is a difference.


What to do now?

This is where you come in. Unless a significant fraction of end users take this stuff seriously, nothing will change. Maybe you're okay with that. If you're not okay with it, and you'd like more refined tools with which to explore the brain, let your suggestions flow. Do we need a committee? If so, should it be run through the OHBM as the COBIDAS has been? Or, can we form a coalition of the willing, a virtual committee that agrees on a basic structure and divides the work over the Internet? We have a lot of online tools at our disposal today.

I envisage some sort of merit badges for methods that have been properly documented, tested and then validated independently. There will necessarily be some subjectivity in determining when to assign a merit badge, but we're after better methods not perfect methods.

How might COBIDAcq work in practice? I think we would have to have some sort of formal procedure to initiate a COBIDAcq review. Also, it's harder to review a method without at least partial input from the developer, given that we might expect some of the documentation to come from them. In an ideal world, new method developers would eagerly seek COBIDAcq review, forwarding mountains of documentation and test data to expedite the next phase. Yeah, okay. Unrealistic. In the mean time, maybe we do things with as much democracy as we can muster: select for review the methods that are getting the most play in the literature.

One criticism I can envision runs along the line of "this will stifle innovation or prevent me from taking on a new method while I wait for you bozos to test it!" Not so. I'll draw a parallel with what the folks did for registered reports. Not all analyses have to be preregistered. If you don't know a priori what you'll do, you are still free to explore your data for interesting effects. So, if you choose to adopt a method outside of the scope of COBIDAcq, good luck with it! (Please still report your methods according to the COBIDAS report.) Maybe you will inadvertently provide some of the validation that we seek, in addition to discovering something fab about brains!

Nothing about this framework is designed to stop anyone, anywhere from doing precisely what they do now. The point of COBIDAcq is to create peer review of methods as early in their lifetime as possible, and to provide clear signaling that a method has been looked at in earnest by experts. Neuroscientists would then have another way to make decisions when selecting between methods.

Okay, that will do. I think the gist is clear. What say you, fMRI world?


Monitoring gradient cable temperature

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While the gradient set is water-cooled, the gradient cables and gradient filters still rely upon air cooling in many scanner suites, such as mine. In the case of the gradient filters, the filter box on my Siemens Trio came with an opaque cover, which we replaced with clear plastic to allow easy inspection and temperature monitoring with an infrared (IR) thermometer:

The gradient filter box in the wall behind my Siemens Trio magnet. It's up at ceiling height, in the lowest possible stray magnetic field. The clear plastic cover is custom. The standard box is opaque white.


Siemens now has a smoke detector inside the gradient filter box, after at least one instance of the gradient filters disintegrating with excess heat. Still, a clear inspection panel is a handy thing to have.

The gradient cables between the filter box and the back of the magnet can also decay with use. If this happens, the load experienced by the gradient amplifier changes and this can affect gradient control fidelity. (More on this below.) The cables can be damaged by excess heat, and this damage leads to higher resistance which itself produces more heating. A classic feedback loop!


The Fluke 561 IR thermometer and a K type thermocouple, purchased separately.


Monitoring both the gradient filters and cables is as easy as purchasing an IR thermometer and some thermocouples. We have a Fluke model 561 IR thermometer (above), costing about $200, which has three nice features. Firstly, it can be used fairly safely inside the magnet room. The unit uses two AA batteries. There is almost no noticeable force on the unit until you take it right into the magnet bore. In well-trained hands it is perfectly safe to use around a 1.5 T or 3 T magnet. It will also perform flawlessly in the fringe field of a 3 T magnet.

The second feature is it's main one: the IR sensor. A laser sight allows easy targeting. This permits quick surface thermometry of the cables, as shown in the photo below, and also of the gradient filters if you have a clear cover like I do. There is a surprising amount of temperature variation along the cables, I find, so having the ability to sweep along a cable can be useful.



The third feature is something you might well skip for simplicity, but I like it. The Fluke is compatible with K type thermocouples. They plug right into the top:


We have installed six thermocouples inside the gradient filter box, one per cable terminal. We used Kapton heat resistant tape to mount them. You can see the tape in the uppermost photo, as nearly horizontal brown bands on the white gradient cable sleeves. Monitoring is as simple as plugging in the desired plug and pulling the trigger on the meter. The Fluke then displays the temperature of the thermocouple rather than of the IR sensor.

K-type thermocouples connected to the six cable terminals inside the filter box. The active ends, taped to the cables, can be seen in the uppermost photograph. We leave the thermocouples installed and simply tuck them out the way when they are not in use.


Using gradient cable and filter thermometry

At the moment I only measure gradient cable temperatures when I'm running long diffusion scans and I want to be sure that I'm not breaking anything. But it would be very easy to incorporate these measurements into routine Facility QA. I would record the starting and ending temperatures of the thermocouples I have taped into place, for consistency. And of course I'd use a constant acquisition protocol; perhaps a diffusion imaging scan to increase the gradient duty cycle and really drive the system. (Right now my Facility QA consists of three ~6 min EPI runs, so only the readout gradient axis has a reasonably high duty cycle, while the other two channels aren't used enough to provoke much departure from room temperature.)

We had to have our gradient cables replaced once because of runaway resistances. For certain diffusion scans we could see cable temperatures over 60°C. But at the time we didn't have the thermocouples installed. We were only alerted to the possibility of a cable resistance/heating issue when our gradient control became unpredictable. We would occasionally see changing levels of distortion in EPI scans; sudden stretches or compressions unrelated to subject movement. (These aren't my data but there is a near identical example posted here.) Had we been monitoring the gradient cable temperatures weekly, we might well have seen a trend towards increasing cable temperatures before the intermittent distortion reported by users, and been in a position to alert the service engineer.

With any luck you will notice the gradient control issues as your first symptom that something is wrong. In the extreme, however, you may find that the gradient connectors decay under the extreme heat. (See the second and third photos in this earlier post on fires in MRI facilities.) By the time your filter connectors are turning to dust you will likely be experiencing occasional spiking events in EPI. It might be externally generated noise that is being conducted into the magnet room by virtue of insufficient RF filtering, or spikes might be generated at the hot connectors. Either way, it's a very good idea to catch the problem long before it gets to this stage!

In future, perhaps the scanner manufacturers will apply water cooling to the gradient cables, as they do already for the gradient and RF amplifiers, plus the gradient set itself, of course. The gradient filters may be at particular risk if, depending on their housing, there is limited airflow. On our unit the filters are designed to cool conductively via the colder equipment room air conditioning. The gradient cables in the magnet room rely upon the magnet room air, which in my facility is at 17°C. Even then, it is quite easy to get >40°C on the surface of the gradient cables with a 20 minute diffusion scan. It's worth looking into.

FMRI data modulators 3: Low frequency oscillations - part I

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Low frequency oscillations (LFOs) may be one of the the most important sources of signal variance for resting-state fMRI. Consider this quote from a recent paper by Tong & Frederick:
"we found that the effects of pLFOs [physiological LFOs] dominated many prominent ICA components, which suggests that, contrary to the popular belief that aliased cardiac and respiration signals are the main physiological noise source in BOLD fMRI, pLFOs may be the most influential physiological signals. Understanding and measuring these pLFOs are important for denoising and accurately modeling BOLD signals."

If true, it's strange that LFOs aren't higher on many lists of problems in fMRI. They seem to be an afterthought, if thought about at all. I suspect that nomenclature may be partly responsible for much of the oversight. A lot of different processes end up in the bucket labeled "LFO." The term is used differently in different contexts, with the context most often defined by the methodology under consideration. Folks using laser Doppler flow cytometry may be referring to something quite different than fMRI folks. Or not. Which rather makes my point. In this post I shall try to sort the contents of the LFO bucket, and in at least one later post, I shall dig more deeply into "systemic LFOs." These are the LFOs having truly physiological origin; where the adjective is used according to its physiological definition:


The description I pulled up from the Google dictionary tells us the essential nature of systemic LFOs: at least some of them are likely to involve the blood gases. And I'll give you a clue to keep you interested. It's the CO component that may end up being most relevant to us.


What exactly do we mean by low frequency oscillations anyway?

"Low frequency" generally refers to fluctuations in fMRI signal that arise, apparently spontaneously, with a frequency of around 0.1 Hz. The precise range of frequencies isn't of critical importance for this post, but it's common to find a bandwidth of 0.05 - 0.15 Hz under discussion in the LFO literature. I'll just say ~ 0.1 Hz and move on. I added "apparently spontaneously" as a caveat because some of mechanisms aren't all that spontaneous, it turns out.

For the purposes of this post we're talking about variations in BOLD signal intensity in a time series with a variation of ~ 0.1 Hz. There may be other brain processes that oscillate at low frequencies, such as electrical activity, but here I am specifically concerned with processes that can leave an imprint on a BOLD-contrasted time series. Thus, neurovascular coupling resulting in LFO is relevant, whereas low frequency brain electrical activity per se is not, because the associated magnetic fields (in the nanotesla range, implied from MEG) are far too small to matter.

Is LFO the lowest modulation of interest? No. There are physiological perturbations that arise at even lower frequencies. These are often termed very low frequency oscillations (VLFOs) because, well, we scientists are an imaginative bunch. These VLFOs generally happen below about 0.05 Hz. The biological processes that fluctuate once or twice a minute may well be related to the LFOs that are the focus here, but I am going to leave them for another day.


Categorizing LFOs:  How do they originate?

There is a lot of terminology in use, much of it confusing. After reading a few dozen papers on various aspects of LFOs, I decided I needed to sort things out in my own way. Different fields may use similar terms but may mean slightly different things by them. Generally, the nomenclature changes with the methodology under consideration. An LFO identified with transcranial Doppler ultrasound in a rat brain may not be the same as an LFO observed with optical imaging on a patient's exposed cortical surface during surgery. Reconciling these differences with LFOs observed in fMRI may be quite misleading as a result.

I finally decided on the four categories of LFO you find below. They are defined in an fMRI-centric way. My goal was to identify the irreducible parts, then try to figure out how different papers use varying nomenclature to discuss the specific mechanisms involved. Hopefully, this allowed me to separate processes in a useful manner from the perspective of an fMRI experiment, since much of the literature on physiological LFOs uses non-MRI methods. To help me relate the processes to fMRI specifically, I resorted to thought experiments. I will include a few in the footnotes so you can check my categorizations. Hopefully, if I have incorrectly characterized or omitted a process, it will be more apparent this way.

1. Instrumental limitations

These do not count as true biological LFOs according to my scheme. The most common way to produce variance around ~0.1 Hz in fMRI is through aliasing. We know that if we are acquiring a volume of EPI data every 2 seconds then we are below the Nyquist sampling frequency for normal human heart rates. Some fraction of the respiratory movements might also end up aliased into our frequency band of interest. By assuming an ideal acquisition method that acquires a volume of data not less than twice per heart beat, we begin to eliminate this source of LFO from our fMRI data. (SMS-EPI may permit sufficiently rapid sampling, depending on voxel size.) Which is why I think it is important to separate fundamentally biological processes from things that are fundamentally scanner-based. I contend that sampling rate is a scanner property, and it it is only the interaction of the biology with an imperfect scanner that produces the LFO. Improvements in scanner design and/or pulse sequences will ameliorate these effects.

An unstable patient table that deflects with a subject's breathing is clearly an instrumental limitation. A rock-solid patient bed eliminates mechanical deflections. Perturbation of B₀ from a subject's breathing is another instrumental limitation. There are a few potential solutions in principle. For example, we could use a field tracker that prevents modulation of the magnetic field over the head from chest motion. Or, if we had a pulse sequence other than EPI, with its low bandwidth in the phase encoding dimension, we could render respiration-induced modulations vanishingly small. (See Note 1.) The important point is that as scanner hardware and sequences are improved, we can expect to make significant advances in the amelioration of these pseudo-biological LFOs.

2. Cardiorespiratory mechanics

I apologize for the clunky term. Cardiopulmonary mechanics was another option. Not much better, huh? In this category are processes that derive from body mechanics; that is, the mechanical processes of physiology that originate outside of the brain. The two main sources are a pumping heart and a set of lungs oxygenating the blood. We seek the biological consequences in the brain that are produced by these oscillating organs. (I can't think of other body organs driving any pulsations but I await being enlightened in the comments section.) We have blood pressure waves and respiration-induced CSF pressure changes via the foramen magnum. These processes are independent of whether we are studying a person by fMRI or using any other method. See Note 2 for some thought experiments I used to derive this category.

The most important cardiorespiratory LFO I've seen in the literature is called the Mayer wave. The commonly accepted definition of a Mayer wave is an arterial blood pressure that isn't constant from heart beat to heart beat, but fluctuates about a resting mean. The fluctuations about the mean arterial BP occur with a frequency of ~ 0.1 Hz. Why the variation? It seems to be related to sympathetic nervous system activity. In lay terms, your "fight or flight" response isn't flat, but very slightly modulated.

The Mayer waves act at the speed of the arterial blood pressure wave. The effect on the BOLD signal happens as fast as the pressure wave passes through the vascular tree, which we know from a previous post can be estimated with the pulse transit time. At most it takes a few hundred milliseconds for the pressure wave to reach the toes from the aorta. We can expect differences of tens of milliseconds in arrival time across the brain, faster than the typical sampling rate of an fMRI experiment.

Can we measure it? The Mayer wave is a change in blood pressure, necessitating a good estimate of BP if we are to get a handle on it. We saw in an earlier post that measuring BP non-invasively in the scanner is non-trivial, however, so we shall have to leave isolation of Mayer waves to some future date. In the mean time, I am not unduly worried about Mayer waves as a major source of LFO because, as I shall claim below, there is likely a far more significant process afoot. 

I don't know enough about respiration-induced pulsation of CSF to estimate the importance of this mechanism at frequencies of ~ 0.1 Hz, except to say that any effects that do exist will be greatest around the brainstem, and will likely decrease the farther one gets from the foramen magnum. As with Mayer waves, I think it's safe to assume that we should worry about other mechanisms first, unless you are doing fMRI of brainstem structures, in which case you should hit the literature and keep this process top-of-mind.

3. Myogenic processes 

The third candidate LFO mechanism is vasomotion. Perturbations in the vascular tone - the tension in the smooth muscle of blood vessel walls - may vary over time. Some of the non-neural signaling mechanisms contributing to vasomotion are reviewed here. The effect is myogenic, meaning "in the muscle."

We assume that vasomotion occurs independent of the contents of the blood in the vessel. Many references also suggest that vasomotion occurs independent of nervous control. In other words, there would be some sort of local oscillatory signaling within the vessel wall that produces an idling rhythm. Additionally, however, vasomotion may be influenced by nervous system responses because the smooth muscles of the arterial walls are innervated. Indeed, this is how we get neurovascular coupling. Thus, some vasomotions might actually be responsible for the target signals in our resting state scans, as suggested very recently by Mateo et al. (See also this 1996 article from Mayhew et al.) So, for the purposes of this post, I shall consider vasomotion as a desirable property, at least for resting state fMRI, and leave the issue of any non-neural components of vasomotion for another day. As things stand, it would be nigh on impossible to separate, using current methods, the target vasomotion - that driven by neurovascular coupling - from any non-neural vasomotion that one might label as a contaminant.

4. Blood-borne agents

A fourth category of LFOs was suggested relatively recently. Mayer waves and vasomotion were observed long before fMRI came about. But it was the advent of resting state fMRI that seems to have precipitated the interest in this category. Blood constituents are not stationary. Instead, the concentration of blood gases - oxygen and carbon dioxide in particular - vary based on your rate and depth of breathing, your stress level, and so on. Anything traveling in the blood that either directly or indirectly mediates BOLD signal changes is therefore of concern, and is included in this category.

The spatial-temporal propagation of LFOs through the brain, arising from blood-borne agents, is naturally at the speed of the bulk blood flow. Whereas Meyer waves propagate through the brain with the velocity of the blood pressure wave, agents carried in the blood tend to move much more slowly. We usually use a mass displacement unit for cerebral blood flow (CBF), typically milliliters of blood per fixed mass of tissue per minute.  But that's not very intuitive for this discussion. Instead, consider the average time taken for blood to transit the brain, from an internal carotid artery to a jugular vein. In normal people this journey takes 7-10 seconds. This is the timescale of relevance to LFOs produced by blood-borne agents.

The most important vasodilative agent carried in the blood is carbon dioxide. It is so important that I am dedicating the entire next post - part II - to it. I hadn't expected to be digging into CO effects until later in this series, since I had anticipated that all the main LFO effects would be vascular, with no direct overlap to respiratory effects. Live and learn. It's a timely reminder of just how complex and interwoven are these physiologic confounds.


Summing up the categories

Okay, to summarize, we have instrumental limitations, which could be eliminated in principle, then three categories of LFO arising out of a subject's physiology. The latter three categories can be expected to occur regardless of the particular MRI scanner you use. These physiological mechanisms arise spontaneously; there is no need to evoke them. Thus, it means they are likely ubiquitous in both resting and task fMRI experiments. 

The pulsatile effects of cardiorespiratory mechanics don't seem to be amenable to independent measurement at the present time. We can possibly infer them from the fMRI data, but then we are forced to deal with the consequences of aliasing and any other instrumental limitations that produce signal variance derived from cardiac or lung motion, manifest via different pathways.

We also don't seem to have a way to separate in principle any non-neural vasomotion from that which may be driven by neurovascular coupling. Multi-modal, invasive measurements in animals, such as performed by Mateo et al., may be the only way to discriminate these processes.

That leaves blood-borne agents. Changes in oxygen tension may be important since, for a fixed metabolic rate of oxygen consumption, any process that alters the supply of oxygen in arterial blood necessarily produces a concomitant change in deoxyhemoglobin in venous blood. I am still investigating the potential importance of oxygen tension, but based on several converging lines of evidence, it appears that fluctuations in arterial CO are the far bigger concern.

Coming up in Part II: Systemic LFOs arising from changes in arterial CO (we think).


__________________________


Notes:

1. If you don't like my field tracker ideal, try this out instead. Imagine we have an fMRI scanner that operates at a main magnetic field of 100 microtesla (μT). A 3 ppm field shift at 3 T equates to nearly 400 Hz; a staggeringly vast frequency shift that would cause horrendous distortions and translations in EPI. But a 3 ppm shift at B₀ = 100 μT corresponds to a frequency of just over 0.01 Hz, against a typical linedwidth of ~20 Hz. The magnetic susceptibility due to chest movement vanishes at this low field. Thus, an ultralow field MRI scanner is robust against the modulation of B₀ from chest movements. The corollary? High field, whole body scanners exhibit enhanced sensitivity to chest movement. (3 ppm at 7 T is a frequency of almost 1 kHz. Ouch.)

2. Imagine we stopped the subject's heart and chest motions and instead replaced the biological functions of heart and lungs with a machine that scrubbed CO₂ and oxygenated the blood before recirculating it through the arteries. It does this in smooth, continuous fashion, without pulsations of any kind. If the machine delivers oxygenated blood to the brain at the same effective rate as the brain needs, all should be okay and the brain should continue to behave normally. But what would happen to the cardiorespiratory mechanical effects? If the machine is ideal, if it doesn't pulse at all, and there are no moving parts to produce any sort of pressure wave through the body, we would have successfully eliminated two sources of LFO.

An alternative way to think about LFOs arising from cardio-respiratory mechanics is to note that the pulsations are independent of the substances being manipulated. Pretending for a moment that the biology wouldn't mind, the mechanical effects across the brain would be the same if the heart was pumping olive oil instead of blood and the lungs were inspiring and expiring pure helium instead of 20% oxygen. The respiratory and cardiac mechanical processes would continue unabated, as would any LFOs produced in our fMRI data, because they arise from the pulsations inherent in the plumbing.


FMRI data modulators 3: Low frequency oscillations - part II

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In the previous post, I laid out four broad categories of low frequency oscillation (LFO) that arise in fMRI data. The first three categories are mentioned quite often in fMRI literature, with aliasing of respiratory and cardiac pulsations being the best known of all “physiological noise” components. In this post, I am going to dig into the fourth category: blood-borne agents. Specifically, I want to review the evidence and investigate the possibility that non-stationary arterial CO₂ might be producing an LFO that is at least as important as aliased mechanical effects. At first blush, this is unsurprising. We all claim to know CO₂ is a potent vasodilator, so we can think of CO₂ in blood as a sort of changing contrast agent that perturbs the arterial diameter – producing changes in cerebral blood volume - whenever the arterial CO₂ concentration departs from steady state.

Why would arterial CO₂ fluctuate? Why isn't it constant? Simply put, we don't breathe perfectly uniformly. If you monitor your own breathing you’ll notice all sorts of pauses and changes of pace. Much of it depends on what you’re doing or thinking about, which of course gets right to the heart of the potential for fluctuations in CO to be a confound for fMRI.

I had hoped to begin this post with a review of CO transport in the blood, and from there to relay what I’ve found on the biochemical mechanism(s) underlying vasodilation caused by CO. But after several weeks of searching and background reading, I still don’t have sufficient understanding of the biochemistry to give you a concise overview. The CO transport mechanisms are quite well understood, it seems. But how a change in one or more components of CO in arterial blood produces changes in the arterial smooth muscle wall, that is a more complicated story. For the purposes of this post, then, we shall have to content ourselves with the idea that CO is, indeed, a potent vasodilator. The detailed biochemistry will have to wait for a later post. For those of you who simply can’t wait, I suggest you read the review articles given in Note 1. They aren’t aimed at an fMRI audience, so unless you are a biochemist or physiologist, you may not get the sort of intuitive understanding that I have been searching for.


First indications that arterial CO might be an important source of LFO in fMRI data

The effects of respiration on BOLD data were recognized in the mid-nineties as an important consideration for fMRI experiments. By the late nineties, several groups began to investigate the effects of intentionally held breaths on BOLD signal dynamics, using as their basis the phenomenon of arterial CO as a vasodilator. Other groups (e.g. Mitra et al., 1997) observed low frequency fluctuations in BOLD data that suggested a vasomotor origin, or found fluctuations in cerebral blood flow (CBF) measured by non-MR means (e.g. Obrig et al., 2000). It wasn’t until 2004, however, that Wise et al. showed definitively how slow variations of arterial CO concentration were related to, and likely driving, low frequency variations in BOLD time series data:
PETCO-related BOLD signal fluctuations showed regional differences across the grey matter, suggesting variability of the responsiveness to carbon dioxide at rest.”
“Significant PETCO-correlated fluctuations in [middle cerebral artery] MCA blood velocity were observed with a lag of 6.3 +/- 1.2 s (mean +/- standard error) with respect to PETCO changes.”

The spatial-temporal dynamics observed by Wise et al. certainly fit a blood-borne agent. That is, we should expect lag variations dependent on the total arterial distance between the heart and the tissue of interest; in their case, the MCA.

A note about nomenclature, and an important assumption. Wise et al., and many others since, used the peak partial pressure of CO, a measure of concentration, that is known as the “end tidal” CO - PETCO - in the expired breath as an estimate of the partial pressure of CO in the arterial blood, the PaCO. This assumption is based on the lung gases and arterial blood gases being in equilibrium. Clearly, there can be regional differences in blood gases all around the body, but to a first approximation we assume that PETCO reflects PaCO.


How do systemic LFOs relate to BOLD signal changes in brain?

In 2000, Obrig et al. used functional near-infrared spectroscopy (fNIRS), comprising a single light source and detector pair placed on the occipital lobe, over visual cortex, to show that an intrinsic LFO of oxyhemoglobin could be detected with or without visual stimuli. (See Note 2 for a brief introduction to NIRS principles.) The LFO was attenuated by hypercapnia when subjects breathed 5% CO in air, a result that matched earlier findings by Biswal et al. in 1997. Since the largest fraction of oxyhemoglobin is arterial, the reduction of LFO intensity when inhaling CO suggests a connection between LFOs and arterial CO concentration. Vasodilation is expected to increase CBV towards its ceiling and reduce the capacity for fluctuations. Intriguingly, Obrig et al. also reported that LFO could be detected in signals originating from deoxyhemoglobin at a magnitude about one tenth those in oxyhemoglobin. These fluctuations apparently preceded the LFO in oxyhemoglobin by 2 seconds, although I would now interpret the deoxy- fluctuation as lagging the oxyhemoglobin by 9-10 sec instead. (Justification for reinterpretation of the Obrig result will become clear later.) The important point is that their data showed LFOs in signals from species found predominantly in arterial as well as venous compartments.

In 2010, Tong & Frederick published the first in a series of studies investigating the spatial and temporal characteristics of LFOs in fMRI data. Functional NIRS was recorded simultaneously with resting state fMRI. The time course of NIRS obtained from the right prefrontal cortex was used as a reference signal to explore the spatial-temporal relationship between NIRS and the entire whole brain fMRI data on a voxel-wise basis. Two forms of NIRS data were used in separate analyses. Signal from oxyhemoglobin is expected to be positively correlated with fMRI signal, being dominated by changes in CBV and CBF. Signal from deoxyhemoglobin arises mostly in venous blood, and its concentration is expected to be inversely correlated with the fMRI data, assuming the standard BOLD model of activation. A NIRS time series was resampled then compared to the fMRI data using shifts of the NIRS data over a range -7.2 to +7.2 seconds, with shift increments of half the TR for the fMRI, i.e. 0.72 sec. Correlations with a positive time shift indicate that an event in the fMRI precedes detection in NIRS data, while negative shifts indicate a lag in the fMRI. Here is an example from one subject, using the oxyhemoglobin signal from NIRS, with a small red circle depicting the approximate location of the NIRS probe being used to measure the reference signal:

Figure 4 from Tong & Frederick, 2010. (Click to enlarge.)

Two features are immediately apparent: there are widespread spatial correlations between NIRS obtained from a single location (at the red circle) to the fMRI detected over the entire brain, and these spatial correlations change with the time lag. It would have been eminently reasonable to expect correlations only at the spatial location sampled by NIRS; perhaps 1-2 cm of cortex. Yet we see correlations throughout the brain and a changing dependence on lag. Take, for example, the bright yellow signal in the superior sagittal sinus (SSS) seen in the left panel at time 0.0 s (green box). Staying with the sagittal view of the left panels, look at what happens to the SSS signal at successively later times. The bright yellow region seems to “flow” downward, from parietal to occipital, until at time 4.32 s there is just a small yellow dot remaining at the occiput. If you have the patience, you can divine similar flow patterns between other time windows for other parts of the brain, as described in the paper:

“From the sagittal view of the z-maps, the BOLD signal wave starts to appear at locations near the callosomarginal, frontopolar and parietooccipital arteries [-5.04 s]. As time progresses, the wave becomes widespread in the gray matter [e.g. -2.16 s], as it passes through capillary beds and then retreats towards the venous systems through several paths, including: 1) the superior cerebral vein to the superior sagittal sinus (also visible from the coronal view) [e.g. 1.44 s]; 2) the inferior sagittal sinus combining internal cerebral vein to the straight sinus; 3) through the transverse sinus (visible in the coronal view); 4) through the anterior and posterior spinal veins. The path the wave follows through the brain strongly resembles that of the cerebral vasculature.”

That last sentence is crucial. The period -5.04 s to +4.32 s, approximately 9 seconds, compares well with the time taken for full passage of blood through the brain. A blood-borne origin is implied. You can even see deep brain correlations occurring again from +5.04 s to +7.2 s in the figure above, while the spatial distribution at +7.2 s resembles that at -4.32 s. Beyond +5.04 s we may be observing correlations of the current LFO period as sampled by NIRS, with the subsequent LFO sampled by the fMRI, since there are usually patterns in how one breathes.

With the NIRS setup over frontal lobe, Tong, Bergethon & Frederick (2011) found that breath holds causing brief hypercapnia produced the same sorts of spatially varying optimal lags with a NIRS signal as had resting state fMRI data, supporting the assignment of a blood-borne agent as the cause. So far so good.

The McLean group then did something inspired: they changed the position of the NIRS sensor to the periphery. This is sound logic if the LFO is systemic – literally, throughout the body – as they suspected it was. So, in their next experiment they added further NIRS sensors to their setup so that they could record from fingers and/or toes at the same time (Tong et al. 2012). This is how NIRS from a finger and toe compare:

Figure 1 from Tong et al., 2012. (Click to enlarge.)

There is a striking similarity in the time courses, except that the signal at the toe lags that detected at the finger. The differing hemodynamic delays in the periphery are nicely exemplified by a comparison of the lags between a finger and a toe versus between the two big toes:
“The LFO signal reaches the [left big] toe 2.16–4 s later than the finger (time delays: Tdelay = 3.07 ± 0.81 s). For three participants, NIRS data was also collected at the right big toe; the LFOs from the two toes had maximal correlations (rmax = 0.85 ± 0.09) with small time shifts between sides (Tdelay = -0.02 ± 0.57 s).”

The greater distance from the heart to toes than from the heart to fingers explains these results nicely. Naturally, the two big toes should exhibit comparable vascular transit times. This is exceedingly strong evidence of a systemic, blood borne perturbation of arterial blood volume.

From comparisons between sites in the periphery using NIRS alone, Tong et al. moved to comparing NIRS recorded from a fingertip to fMRI recorded simultaneously from the brain. These results were consistent with their earlier correlations produced with NIRS on the forehead:
“First, the voxels, which are highly correlated with NIRS data, are widely and symmetrically distributed throughout the brain, with the highest correlation appearing in the draining veins, although there is also significant correlation throughout the gray matter. This global signal confirms that a significant portion of the LFO signal in the brain is related to systemic blood circulation variations. Second, the dynamic pattern reflects the variable arrival times of the LFOs at different parts of the brain, just as it arrives at the finger and the toe with different time delays. This latter observation supports the contention that the LFO signal directly reflects bulk blood flow and confirms our previous, brain-only measurements.”

We know that aliased cardiac and respiratory frequencies are a major problem for fMRI with slow sampling, i.e. long TR. Here, however, the reference time course is from NIRS sampled well above the Nyquist frequencies of both processes, allowing Tong et al. to make an important inference:
“Another observation from the present results is that because the LFO used in [regressor interpolation at progressive time delays] RIPTiDe is derived by applying a bandpass filter (0.01 to 0.15 Hz) to the NIRS Δ[tHb], which has been sampled at a relatively high frequency (12.5 Hz), the heartbeat (~1 Hz) and respiratory (~0.2 Hz) signals have been fully sampled; therefore there is no aliasing of these signals into the LFO signal. Consequently, the LFOs we identified in the periphery, and those we identified in the brain with BOLD fMRI, are independent of the fluctuations from the cardiac pulsation (measured by pulse oximeter) and respiration (measured by respiration belt), which provides strong counterevidence to the contention that the non-neuronal LFO in BOLD is mainly the aliased signal from cardiac pulsation and respiration.”

It is striking to me that some amount of LFO is systemic. Tong et al. didn’t (dare?) venture a candidate blood-borne agent in their 2012 study, although they must have had strong suspicions. But, as we shall see momentarily, by 2014 they were suggesting arterial CO as a good explanation. Let’s assume it is arterial CO, although the implication is the same whatever the agent: there is a mechanism for producing vasodilation in the walls of peripheral arteries, just as there is in cerebral arteries. Is that surprising? It isn’t something I would have assumed to be necessarily the case, but I’m not a physiologist. The brain, muscles and dermis could all have evolved quite different sensitivity to arterial CO, if there were unique implications for local metabolism. That seems not to be the case. Instead, there is a generalized sensitivity to arterial CO that produces vasodilation. And one consequence of this generalized response is a systemic LFO that can be detected anywhere in the body, including in the brain.


Doing away with the extra hardware

Recording NIRS requires custom hardware. (See Note 3.) For their next trick, Tong & Frederick managed to do away with the need for the NIRS hardware altogether. In 2014, they presented a data-driven version of their RIPTiDe method for mapping lags:
“In this study, we applied a new data-driven method to resting state BOLD fMRI data to dynamically map blood circulation in the brain. The regressors used at each time point to track blood flow were derived from the BOLD signals themselves using a recursive procedure. Because this analytical method is based on fMRI data alone (either task or resting state), it can be performed independently from the functional analyses and therefore does not interfere with the fMRI results. Furthermore, it offers additional information about cerebral blood flow simultaneously recorded with the functional study.”

A bandwidth 0.05 – 0.2 Hz was investigated in resting state data obtained at a TR of 400 ms (using MB-EPI) to ensure sampling of mechanical respiratory and cardiac fluctuations above the Nyquist frequency. Large blood vessels clear of brain tissue were identified in the raw data – for example, the carotid arteries or jugular veins passing through an inferior axial slice, or the superior sagittal sinus in a sagittal slice – and these vessels were used to define a seed region. The time course from a single voxel in a large vessel is designated the reference regressor: the regressor with zero lag. After voxelwise cross correlations with the reference regressor, a new time series regressor is determined. The time series selected has the highest cross correlation with the original (zero lag) regressor at a temporal offset of one TR. This “moves” the regressor through time by one TR, tracking the propagation of the fluctuations inherent in the original time series. The spatial origins of the new regressor don’t matter. The new regressor comprises the time series of all voxels that obey an appropriate threshold criterion. A second cross correlation is then performed, searching for voxels that give the highest correlation with the second regressor time series, but at a further offset of one TR (which is now two TRs away from the reference regressor). The process repeats until the number of voxels selected as the strongest cross correlation, offset by one TR, is less than some predefined number.

The iterative procedure can be applied in reverse; that is, the temporal offset between the reference regressor and the next time series is set to be –TR. A negative lag simply means that the cross correlation will be maximized for fluctuations in the search time series that precede fluctuations in the reference time series. Thus, one may iterate forwards (positive TR lags) or backwards (negative TR lags) in time, relative to the start point. Refinement of the seed selection can also be made based on the results of a first pass through the data. One can even use the time series corresponding to the highest number of voxels obtained in a first pass as the optimal seed regressor for a second analysis; a form of signal averaging. In part b of the figure below, a blue circle indicates that the number of voxels sharing fluctuations with a single voxel seed is quite small; only 200-300 voxels. A black circle indicates the set of voxels to be used in a second, optimized analysis. There is a set of 5000 voxels that have common fluctuations in the band 0.05 – 0.2 Hz.

Whether a single voxel seed or some optimized, averaged seed is used, once a full set of regressor waveforms has been produced recursively, the entire set is used in a GLM to produce z maps of the voxel locations for each lag. An example is shown in part c of this figure:

Figure 2 from Tong & Frederick, 2014. (Click to enlarge.)


Tong & Frederick tested their method in a variety of ways. The results were reassuringly robust to seed selection. This makes sense for a biological process – blood flow – that is evolving smoothly in time.

The dynamic maps produced by the data-driven method resemble those produced in earlier work using a NIRS reference signal:
“The LFOs are “piped” into the brain though big arteries (e.g., internal carotid artery) with no phase shift. They then follow different paths (arterioles, capillaries, etc.) as branches of the cerebral vasculature diverge. It is expected that each signal would evolve independently as it travels along its own path. The observation that some of them have evolved in a similar way, and at a similar pace, is probably due to the uniformity in the fundamental structures of the cerebral blood system, likely reflecting the self-invariant properties of fractal structures found throughout biological systems.”
A delay map - figure below - resembles cerebral circulation, as in earlier work using a NIRS reference. (There are also two compelling videos in the Supplemental Information to the paper.)

Figure 6 from Tong & Frederick, 2014. (Click to enlarge.)



Converging lines of evidence for arterial CO₂ as a cause of systemic LFO

Lag-based analyses of fMRI data provide good evidence that a blood-borne agent is inducing systemic fluctuations at a frequency of ~0.1 Hz. Rhythmic dilation and constriction of pial arterioles at 0.1 Hz has been observed propagating on the exposed cortical surface of a patient undergoing surgery (Rayshubskiy et al., 2014). This is further circumstantial evidence in support of a blood-borne agent of some kind. But mechanisms to explain the source of these LFOs remain speculative. What other evidence is there that variation in PaCO₂, specifically, produces a strong systemic LFO in fMRI data?

Adding to the circumstantial case is the recent work by Power et al. (2017). They were motivated to investigate the empirical properties of the mean global signal in resting state fMRI data, finding variance attributable separately to head motion and hardware artifacts, as well as to the physiological consequences of respiratory patterns. In the absence of large head motion and hardware artifacts, they conclude that most of the remaining variance in the mean global signal is due to respiratory fluctuations, that is, to variations in PaCO₂.

Having observed that common measures of head motion such as framewise displacement (FD) can reflect physiological (i.e. apparent head motion) as well as real head motion effects, Byrge & Kennedy (2017) investigated the spatial-temporal nature of artifacts following changes revealed in the FD trace. They term this the lagged BOLD structure:
“Our general approach is to ask whether there is any common structure in the BOLD epochs immediately following all similar instances of the nuisance signal – specifically, following all framewise displacements within a particular range of values – using a construction similar to a peri-event time histogram. If there is any systematic covariance shared by BOLD epochs that follow similar displacements (within and/or across subjects), such a pattern reflects residual displacement-linked noise that should not be present in a perfect cleanup – regardless of the underlying sources of that noise.”

 “Using this method, we find a characteristic pattern of structured BOLD artifact following even extremely small framewise displacements, including those that fall well within typical standards for data inclusion. These systematic FD-linked patterns of noise persist for temporally extended epochs – on the order of 20–30s – following an initial displacement, with the magnitude of signal changes varying systematically according to the initial magnitude of displacement.”

When the FD is large – perhaps real head motion or an apparent head motion from a deep breath– the BOLD signal attains a negative maximum amplitude some 10-14 sec after the event. But when the FD is small – shallow breaths, perhaps – the BOLD signal produces a positive maximum amplitude at a similar latency. Moreover, the biphasic nature of the BOLD responses in each case also suggests differing mechanisms for differing features. In the case of large FD, there is an initial positive maximum in the BOLD response at a latency of 2-3 sec. But for small FD, the initial response is negative. Figure 1 from their paper is reproduced below. For expediency, you can focus on part (a). The rest of the figure shows that the lagged BOLD structure is observed consistently from two different sites (the rows), and remains in the data after standard preprocessing steps aimed at removing physiological artifacts (the columns). Note the opposite phases for the largest FD (bright yellow) and smallest FD ranges (dark blue):


Figure 1 from Byrge & Kennedy, 2017. (Click to enlarge.)

“The lagged BOLD patterns associated with respiration are not the same as the lagged patterns associated with displacements [i.e. head motion], but their similar temporal and parametric properties are suggestive of the possibility that respiratory mechanisms may underlie some of the displacement-linked lagged structure in the BOLD signal.”

There is another subtle result here. Compare, for example, the darkest blue trace – FD between zero and 0.05 mm – to the bright green trace – FD between 0.35 – 0.4 mm in part (a), above. Counter-intuitively, the smaller FD produce larger subsequent fluctuations in BOLD than some framewise displacements having considerably greater magnitude! So much for eliminating the head motion! If you do that, you reveal another perturbation underneath.

There are several other intriguing results in the Byrge & Kennedy paper. For example, they assess the spatial distribution of the changes depicted in their Figure 1, finding that the structure is largely global. They also find relationships between the lagged BOLD structure and standard models of respiratory effects, especially respiratory volume per unit time (RVT), but minimal association with cardiac measures. Their conclusion is that there are large fluctuations in resting state BOLD data that can be attributed to respiratory effects, and changes in arterial CO₂ is the most plausible explanation. If you have the time, I suggest reading the paper in its entirety. It is extremely thorough and well-written.

Right, it’s time for me to close my case for the prosecution: a contention that variation in PaCO₂ is the proximal cause of systemic LFOs. I want to move on to the consequences of systemic LFOs, however they come about.


How do systemic LFOs affect resting functional connectivity?

A systemic LFO at around 0.1 Hz is a serious potential confound for resting state fMRI, given the common practice of low-pass filtering fMRI data for subsequent analysis. It is widely believed that BOLD fluctuations below about 0.15 Hz represent ongoing brain activity. How much overlap might exist between sLFO and intrinsic brain activity as represented in BOLD data?

In their first investigation into functional connectivity, Tong et al. (2013) used NIRS recorded in the periphery – fingers and toes – to assess the contribution of systemic LFOs in the band 0.01-0.15 Hz to brain networks derived from independent component analysis (ICA). They found that spatial maps of sLFO-correlated BOLD signals tended to overlap the maps of several typical resting-state networks that are often reported using ICA. A subsequent study (Tong & Frederick, 2014) using fMRI data with TR = 400 ms, to avoid aliasing of mechanical respiratory perturbations, found much the same thing. The mechanical respiratory effects could be separated from the systemic LFOs, and the sLFO dominated several prominent independent components.

The earlier studies showed that spatial patterns of sLFO were coincident with resting-state networks commonly reported in the literature. Just how coincidental were those findings? In 2015, Tong et al. inverted the process and set out to determine whether they could establish apparent connectivity in the brain using synthetic time series data having the spatial and temporal properties of systemic LFOs. First, they produced from each subject’s resting state fMRI data a lag map of correlations between a voxel’s time course and NIRS recorded in a finger. This 3D map represents the lag with the strongest correlation between the NIRS signal and each voxel’s BOLD signal. This map was applied to a synthetic BOLD “signal,” comprising sinusoids and white noise. At each voxel, the synthetic time series was scaled by the local signal intensity, and shifted in time using the real lag value produced for the 3D lag map. The spatial-temporal properties of the final synthetic time series thus follow the basic intensity and delay structures of real fMRI data, but are otherwise entirely arbitrary. An example lag map produced using the seed-based regression method is shown below, with the NIRS-based lag map in the inset. (The seed-based and NIRS-based methods generated similar results.) In parts B and C are exemplar synthetic time courses for three voxels with different lags:


Figure 3 from Tong et al., 2015. (Click to enlarge.)

Note that the synthetic data comprises sinusoids band-limited to 0.01-0.2 Hz, the same frequency range as the real data. The lag used at each voxel is derived from a biological measurement, that is, from correlations between real BOLD data and NIRS in the subject’s finger (or, alternatively, from a seed-based regression). In this respect, the lags are biological information, and the lags are encoded into (applied to) the synthetic data. But the only way any neuronal relationships can end up in the synthetic data is if the lags happen to contain neurogenic information in the first place. In the case of a NIRS signal measured in the finger to determine the lag maps, we might concede an autonomic nervous system (ANS) response, perhaps. This is unlikely, however, because the temporal characteristics of the systemic LFOs imply a blood-borne agent, whereas nervous system control over vascular tone ought to be more efficient than waiting for blood to arrive. (See Note 4.) Still, let’s allow the remote possibility of a neurogenic basis for the lags and define any implications. If we eventually learn that the systemic LFOs derive from the ANS and not arterial CO₂ (or some other blood-borne agent), we will then have to consider a highly prominent, concerted ANS response obscuring whatever subtle, regional neural activity we might want to see hiding in the resting-state fMRI data.

Returning to the 2015 paper, the next step was to run group ICA or seed-based correlation analysis, two common approaches to obtain functional connectivity estimates, and assess any false “networks” produced from the synthetic data. These results were compared directly to the same ICA method applied to real fMRI data. In the next figure are eight groups of independent components obtained from spatial correlation with a literature template for resting-state networks. ICs from real data are in the left column, the middle and right columns are ICs derived from the synthetic data created using the seed-based recursive and NIRS reference signal, respectively:


Figure 5 from Tong et al., 2015. (Click to enlarge.)

The good news is that the spatial correlation coefficients (see the numbers above the axial view of each IC) are lower in both sets of synthetic data than for real data. The bad news is that one can clearly recognize “networks” arising out of the synthetic data. (The red boxes highlight two instances of networks that couldn’t be isolated.)

There are also clear similarities in the default mode network returned from a seed-based analysis of real data (left) to that from synthetic data (right):


Figure 6 from Tong et al., 2015. (Click to enlarge.)

Not perfect correspondence, but remarkable consistency. Whether you chose to focus on the similarities or the dissimilarities, we can’t escape an obvious conclusion: systemic LFOs can produce patterns that look like resting-state networks.


How to deal with systemic LFOs in fMRI

The initial approach to de-noising with RIPTiDe, by Frederick, Nickerson & Tong in 2012, used a reference NIRS waveform recorded from the forehead. In a subsequent study, RIPTiDe de-noising was applied based on the NIRS signal from subjects’ fingers (Hocke et al. 2016). This reduces the chance of accidentally capturing neural activity in the NIRS waveform, and simplifies the setup. The NIRS-based method explained twice as much variance in resting-state fMRI data than de-noising methods requiring models of respiration or cardiac response functions. Furthermore, only a small but insignificant correlation was found between NIRS and a respiratory variation model. Most signal power was not shared between NIRS and respiratory or cardiac variation models. These results suggest a different origin for sLFO signals than are measured with conventional respiratory belt or pulse oximetry traces, even though some respiratory models are designed to account for arterial CO₂ fluctuations. Whether multiple de-noising methods should be nested, and in what order, is a subject for a later date.

The use of a reference NIRS signal is still a major limitation, especially for data that are already sitting in repositories for which there may be no peripheral physiological data. The data-driven approach, using seeds developed from the fMRI data themselves, overcomes this. (One can still use a NIRS signal as the initial seed waveform, but it isn’t required.) There is more work to do, but even if the original seed is defined in such a way as to capture neurogenic signals accidentally (or intentionally, if you opt for a gray matter seed), the smooth evolution of the regression procedure over several seconds, followed if desired by the definition of an optimal seed (which will likely represent large draining veins) and a second recursive procedure, should ensure that the final set of regressors doesn’t contain neural activity. So, if you want my advice, I would urge to you read up on the latest developments on Blaise Frederick’s github, and start tinkering.


Conclusions

Circumstantial evidence from several groups suggests that non-stationary arterial CO₂ is responsible for a systemic LFO in fMRI data. The overlap of this systemic LFO with neurogenic fluctuations of interest in resting-state fMRI suggests that a major physiologic “noise” component is being retained in most functional connectivity studies. Some studies may be partly removing sLFO through global signal regression (GSR), but given the spatial-temporal properties of the sLFO, GSR alone is unlikely to clean the data as well as a lag-based method. And there are statistical arguments against GSR anyway. As a compromise, you might consider dynamic GSR, which uses the lag-based properties to model propagation of LFO through the brain with a voxel-specific time delay prior to regression.

RapidTiDe, the accelerated version of the original RIPTiDe method, looks like a useful option for de-noising. The use of the fMRI data to derive seed-based lags and regressors for de-noising should be familiar to anyone who has used the popular CompCor method. No additional measurements are required for RapidTiDe. Most fMRI data should contain sufficient vascular information to permit good seed selection, which should enhance its appeal significantly. Even better, code is available now for you to run tests with!

There are alternative methods that may permit removal of systemic LFOs. I focused on lag-based methods in this post because they provide compelling spatial-temporal demonstrations of systemic LFOs. Collectively, these provide the strongest evidence I’ve found for working under the assumption that the sLFO is due to arterial CO₂. The next step, it seems to me, is to develop routine approaches aimed at accounting for sLFO in resting state fMRI data.

Finally, a quick note on using expired CO₂ traces to get at fluctuations of PaCO₂. Measurement of expired CO₂ is supposed to be the focus of the blog post after next, according to my original list of fluctuations and biases in fMRI data. Until very recently, I had been assuming we would need expired CO₂ measurements to account for changes in PaCO₂. That may still be true, but as my center has been setting up devices to measure expired CO₂, and as I’ve learned more about lag-based methods such as RIPTiDe, my enthusiasm has shifted towards the latter. There are two main reasons for my enthusiasm for RIPTiDe: 1. the data-driven results are striking, and 2. there are practical hurdles to good expired CO₂ data, and some of these hurdles may be insurmountable. The practical hurdles? For a start, you need a dedicated setup that involves using a mask or nasal canula on your subject. Some people aren’t going to like it. Next, getting robust, accurate expired CO₂ data is non-trivial, even when the mask or canula fits perfectly. There are dead volumes in the hoses to consider, amplifier calibration and sensitivity issues, and other experimental factors. Not all breaths can be detected reliably, either. It can be quite difficult to discern very shallow respiration. (I thank Molly Bright and Daniel Bulte for the warnings. You were right!)

Even when all these practical hurdles have been addressed, there’s one final factor that can’t be circumvented: recording expired CO₂ only provides you with data some of the time. You have no knowledge about what’s happening during inspiration, or when the subject holds his breath for a few seconds. Everything the subject does has to be inferred retroactively from the expired breath. All of which suggests to me that other methods should be attempted first. I like the Tong and Frederick approach, especially a seed-based method that uses just the fMRI data. This tactic has worked well for regions of no interest in CSF and white matter, as with the CompCor method. So why not a lag-based method using a seed in the vasculature? Cleaning up systemic LFOs, especially if they are ever proven to arise from CO₂ in the blood, could massively improve the specificity of functional connectivity.

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Notes:

1.  Comprehensive reviews on CO₂ transport in blood, and on cerebrovascular response to CO₂:

Carbon dioxide transport
GJ Arthurs & M Sudhakar
Continuing Education in Anaesthesia Critical Care & Pain, Vol 5, Issue 6, Dec 2005, Pages 207–210
https://academic.oup.com/bjaed/article/5/6/207/331369
https://doi.org/10.1093/bjaceaccp/mki050

The cerebrovascular response to carbon dioxide in humans
A Battisti-Charbonney, J Fisher & J Duffin
J Physiol. 2011; 589 (Pt 12): 3039–3048. 
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3139085/
https://doi.org/10.1113/jphysiol.2011.206052

Some highlights: 
The mechanism by which CO₂ affects cerebrovascular resistance vessels is not fully understood. Increased CO leads to increased [H+], which activates voltage gated K+ channels. The resulting hyperpolarization of endothelial cells reduces intracellular calcium, which leads to vascular relaxation and hence vasodilation.

The mechanism of regulation of CBF is via pial arteriolar tone, since these provide the main resistance vessels.

The mechanism underlying this regulation appears independent of the decreased and increased arterial pH levels accompanying the elevated and lowered pCO
, respectively, since CBF remains unchanged following metabolic acidosis and alkalosis. Rather, findings suggest that CBF is regulated by changes in pH of the cerebral spinal fluid (CSF) as the result of the rapid equilibration between CO in the arterial blood and CSF. The lowered/elevated pH in the CSF then acts directly on the vasculature to cause relaxation and contraction, respectively. Thus, the action of pCO on the vasculature is restricted to that of altering CSF pH, i.e., is void of other indirect effects as well as direct effects. 
But vasodilation is also observed in the periphery where there is no CSF. So, even if this explanation is correct for the brain, I am still left wondering how arterial CO₂ causes vasodilation elsewhere in the body. Let me know if you find a good review, please!

pCO₂ and pH regulation of cerebral blood flow. 
S Yoon, M Zuccarello & RM Rapoport.
Front Physiol. 2012, 3:365.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3442265/
https://doi.org/10.3389/fphys.2012.00365


2.  Dual wavelength near-infrared spectroscopy (NIRS) can be used to estimate the oxyhemoglobin (HbO), deoxyhemoglobin (Hb) concentrations simultaneously. The method works via differential absorption of light at two wavelengths. The wavelengths are selected to provide optimal absorption of the target chromophores - that is, different forms of hemoglobin - and to minimize absorption by water and other tissue components. The total hemoglobin (HbT) concentration can then be deduced using the Modified Beer-Lambert law. It is generally assumed that HbT provides an estimate of CBV, including arterioles, capillaries and venules. The Hb signal arises mostly from veins when the arterial blood is close to 100% saturated, as in normal subjects. The HbO signal arises from both arterial and venous compartments. There are several references and reviews on all this, but nothing I've found so far is a good introduction for a lay audience (like me). I'll keep an eye out.


3.  While NIRS and pulse oximetry are based on the same phenomenon - the absorption of light by blood components - NIRS devices usually differ from pulse oximeters in the wavelength(s) used, as well as in the number and placement of sensors, signal processing (such as high pass filtering for pulse oximetry), and other application-specific considerations.


4.  Here I am ignoring the well-known feedback response to changes in arterial CO₂, since this is the chemoreflex responding to changes in PaCO₂ rather than ANS providing a feed-forward control over local vascular tone. The chemoreflex regulatory mechanism alters the respiration rate and volume of subsequent breaths, to push CO₂ concentration towards an equilibrium value. The total feedback loop can take multiple breathing cycles; tens of seconds. We will see the results of these feedback loops in the fMRI data. Indeed, these are exactly the systemic LFOs that are the focus of this post! So, the ANS is part of the reason for there being a non-stationary arterial CO₂. But it is indirect in the same way that the ANS is also involved in governing the heart rate. When the heart rate changes we don’t claim a direct, neurogenic source of fluctuations in the fMRI data, even though we recognize the crucial role of the ANS in regulating the process. Some of you may be using the heart rate variability as an emotional measure. Perhaps something similar can be done with changes in respiration. In any event, most fMRI experiments are aiming to see something cortical, something beyond the ANS, and so changes in PaCO₂ or in heart rate are at best uninteresting, at worst a nuisance.


Arterial carbon dioxide as an endogenous "contrast agent" for blood flow imaging

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I nearly called this post Low Frequency Oscillations - part III since it closely follows the subject material I covered in the last two posts. But this is a slight tangent. Following the maxim "One scientist's noise is another scientist's signal," in this post I want to look at the utility of systemic LFO to map blood flow dynamics, an idea that was suggested in 2013 by Lv et al. based on the earlier work from Tong & Frederick that I reviewed last post. There is also at least one review of this topic, from 2017.

Let me first recap the last post. There is sufficient evidence, supported by multiple direct and indirect lines of inquiry, to suggest a blood-borne contrast mechanism that produces a prominent fluctuation at around 0.1 Hz in resting-state fMRI data. (Here, I assume a standard T₂*-weighted EPI acquisition for the resting-state fMRI data.) Furthermore, the same fluctuation can be found anywhere in the body. That is, the fluctuation is truly systemic. The best explanation to date is that non-stationary arterial CO₂ concentration, brought about by variations in breathing rate and/or depth, produces changes in arterial tone by virtue of the sensitivity of smooth muscle walls to the CO₂ dissolved in arterial blood. I shall assume such a mechanism throughout this post, while noting that the actual mechanism is less critical here than whether there is some utility to be exploited.

In the title I put "contrast agent" in quotes. That's because the CO₂ isn't the actual contrast agent, but a modulator of contrast changes. When the smooth muscle walls of an artery sense a changing CO₂ concentration, they either expand or contract locally, modulating the blood flow through that vessel. In the brain, a change in a blood vessel's diameter causes a concomitant change cerebral blood volume (CBV), hence cerebral blood flow (CBF). There may be a local change in magnetic susceptibility corresponding to the altered CBV in the arteries and capillaries. But the altered CBF will definitely produce the well-known change in magnetic susceptibility in and around the venous blood that can be detected downstream of the tissue, i.e. the standard BOLD effect. The actual contrast we detect is by virtue of changes in T₂* (for gradient echo EPI), plus the possibility of some flow weighting of the arterial blood depending on the combination of flip angle (FA) and repetition time (TR) being used. As a shorthand, however, I shall refer to arterial CO₂ as the endogenous contrast agent because whenever an artery senses a change in CO₂ concentration, there will be a concomitant change in vessel tone, and we will see a cascade of signal changes arising from it. (See Note 1 for some fun with acronyms!)


Time shift analysis

Most published studies attempting to exploit systemic LFO have used fixed time shifts, or lags, in their analysis. You just need a few minutes' worth of BOLD fMRI data, usually resting state (task-free). The analysis is then conceptually straightforward:
  1. Define a reference, or "seed," time course;
  2. Perform cross correlations between the "seed" and the time course of each voxel, using a set of time shifts that typically spans a range of 15-20 seconds (based on the expected brain hemodynamics);
  3. Determine for each voxel which time shift gives the largest cross correlation value, and plot that value (the delay, in seconds) to produce a lag map.

There are experimental variables, naturally. The duration of the BOLD time series varies, but most studies to date have used the 5-8 min acquisition that's common for resting-state connectivity. Some studies filter the data before starting the analysis. Different studies also tend to choose different seeds. There are pros and cons for each seed category that I assess in the next section. Time shifts are usually increments of TR, e.g. the lag range might be over +/- 5 TRs for a common TR of 2 sec. And, in producing the final lag maps, some studies apply acceptance criteria to reject low correlations.

Let's look at an example time shift analysis, from Siegel et al. (2016). The raw data were filtered with a pass-band of 0.009 - 0.09 Hz. For cross correlations, they used as their seed time course the global gray matter (GM) signal. Cross correlations were computed voxel-by-voxel for nine delays of TR = 2 sec increments, covering +/- 8 sec, followed by interpolation over the lag range. The time shift corresponding to the maximum cross correlation was assigned that voxel's lag value in the final map, as shown here:

Fig. 1 from Siegel et al. (2016).


They define negative time shifts as maximum cross correlations which lead the mean GM signal - the light blue regions in part (c) - and positive time shifts as correlations that lag the mean GM signal. Dark blue represents zero lag, i.e. mostly the GM region used as the seed time course.

What are we to make of the heterogeneity in the lag map in part (c) above? An asymmetry we can understand because this is from a stroke patient. Even so, there doesn't seem to be any clear anatomical distinction in the image. Certainly, some of the red-yellow voxels could represent large draining veins on the brain surface, but there are deeper brain regions that also show up red. What's going on? We need to explore the seed selection criteria in more detail.


How should we choose the seed time course?

With a fixed seed time course to be used as a voxel-wise regressor for the whole data set, there are essentially three situations to consider: a venous seed, an arterial seed, or a brain tissue seed.

Taking the venous seed first, the superior sagittal sinus (SSS) offers a robust BOLD effect and, being on the surface of the brain, can be identified and segmented reasonably easily. Here is a group average lag map produced by Tong et al. (2017) using a seed in SSS (top row) compared to a time-to-peak (TTP) map derived from the first pass kinetics of a bolus injection of gadolinium contrast agent (i.e. dynamic susceptibility contrast imaging):

Fig. 5 from Tong et al. (2017).

Notice how there are more late - that is, venous - voxels (red-yellow) in the lag map produced from the BOLD data (top row) compared to the DSC data (bottom row). The DSC is more heavily weighted towards early arrival, that is, towards the arterial side; more blue areas. And this makes sense because the DSC method is aimed at extracting a perfusion index. The kinetic model used in DSC imaging aims to map the blood arriving in the brain tissue, not the blood leaving the tissue. In other words, DSC is intentionally weighted towards the arterial side of the hemodynamics. The problem with the SSS signal is that it is already quite far removed from whatever happened in the brain upstream. After all, it is blood that has already transited brain tissue and is being directed down towards the jugular veins where it will leave the head entirely. Making strong correlations with arterial flow on the upstream side of the brain is thus a tricky proposition. It can be done, but the complications introduced by the brain tissue in between suggests caution.

What happens, then, if we select an arterial seed instead of a venous seed? Such a comparison was presented recently by Tong et al. (2018) using the MyConnectome data from Russ Poldrack: 90 resting-state fMRI scans collected over a two year period. The internal carotid arteries (ICA), the internal jugular veins (IJV) and the SSS were identified on T₁- and T₂-weighted anatomical scans, since these high-resolution 3D images cover the neck as well as the whole brain. Six time courses were used in time shift analyses: left and right ICA, left and right IJV, SSS, and the global mean brain signal (GS). The time shift range was +/- 15 sec, to ensure full passage of the blood through the head. On average, over the 90 sessions, the maximum cross correlations arose for ICA signals leading GS by between 2.8 and 3 seconds, while the SSS time course lagged the GS time course by 3.6 seconds, and the IJV signals lagged GS by around 4.3 seconds. (There was more scatter in left IJV data than in right IJV.) The accumulated delay from ICA to IJV was 7 to 7.5 sec, consistent with full passage of blood through the head.

Fig. 3 from Tong et al. (2018).

There was, however, an interesting finding. While there was good cross correlation between the ICA and other signals, the ICA was always negatively correlated with the GS, the SSS and IJV (see figure above). That is, the contrast change on the passage of the CO₂ was a signal decrease, not a signal increase as in the downstream regions. This must be a consequence of the particular form of BOLD contrast in the internal carotids. Tong et al. speculate that it is a small change in CBV producing a small extravascular (negative) BOLD signal change from the volume magnetic susceptibility difference between the artery (containing blood near 100% saturated with oxygen) and surrounding neck tissue. This is an interesting technical finding, and it has implications if we want to change the acquisition (see later), but it's also perfectly understandable as a conventional, albeit unusual, form of BOLD contrast.

So, using arterial seeds instead of venous seeds works in a test case. Great! What are the implications for using an arterial seed for perfusion mapping more generally? As with the venous seed, I am primarily concerned with the dynamics once the seed reaches the brain. Clearly, all the blood that is flowing through the internal carotid artery at any moment in time isn't destined for the same brain location or even the same tissue type. Some of the blood in our arterial reference signal ends up in GM, some in WM. The passage of blood is different through these two tissues, imposing different subsequent delay characteristics that are carried through to the venous blood. This is a well-known problem in arterial spin labeling (ASL), where the mean transit time (MTT) is known to differ between GM and WM, as well as with age, and with pathology. In ASL methods, one remedy is to use multiple post-labeling delays and measure a range of MTT rather than relying on a single delay and assuming the entire brain has the same response. Keep this point in mind because I will argue that a fixed lag analysis suffers from the same fundamental problems. Thus, while there are features of an arterial seed that "survive passage of the brain" into the venous system and the draining veins, the brain tissue adds complexity and ambiguity in the form of many potential sources for modulation of the dynamics along the way.

Which brings us to brain tissue as a seed time course. Some groups have used the global mean signal. I am against this on basic physiological grounds: we shouldn't combine the time courses of GM and WM because we know that in a healthy brain the blood flow in GM is 3-5 times higher than in WM. Using a combined GM + WM signal is tantamount to temporal smoothing.

An alternative is to use the GM signal only. This is better, but still not ideal because the GM is modulated by both the sLFO signals that we are trying to measure, plus all sorts of neurovascular modulations due to ongoing brain activity that are the focus of fMRI studies. With a GM seed there is the possibility of feedback effects across the entire GM from changes in arousal, through sympathetic nervous system responses. There will also be local fluctuations depending on the underlying brain activity. Doubtless, some of these fluctuations will be averaged away over the many minutes of a typical acquisition, but we can't assume they will average to zero. Thus, if we take as our reference time course a signal that has neurovascular effects already "baked in," our regression is going to be working simultaneously to assess systemic effects plus at least some fraction of ongoing brain activity. The neurovascular activity is considered "noise" in this interpretation! Lags in GM directly attributable to neural causes are around a second according to Mitra et al. This could be sufficient to cause regional variations that could appear as pathology when assessing patient groups.


Recursive time shift analysis

There is one approach that allows us to overcome many of the aforementioned limitations. And that is to move away from a single seed time course altogether. We need more temporal flexibility, a bit like using multiple transit delays in ASL to compensate for variations in MTT. For lag analysis, the recursive approach developed by Tong & Frederick is an elegant way to "ride along" with the systemic fluctuation as it propagates through the entire vascular system. The basic logic is to look upstream or downstream one TR at a time.

The time course from a single voxel in a large vessel is designated the reference regressor: the regressor with zero lag. After voxel-by-voxel cross correlations with the reference regressor, a new time series regressor is determined. It is the average of the time series of all voxels satisfying a particular cross correlation threshold. The new reference time series has the highest cross correlation with the original (zero lag) regressor at a temporal offset of one TR. This “moves” the regressor through time by one TR, tracking the propagation of the fluctuations inherent in the original time series. The spatial origins of the new regressor don’t matter. The new regressor simply comprises the time series of all voxels that obey an appropriate threshold criterion. A second cross correlation is then performed, searching for voxels that give the highest correlation with the second regressor time series, but at a further offset of one TR (which is now two TRs away from the original time series). The process repeats until the number of voxels selected as the strongest cross correlation, offset by one TR, is less than some predefined number. The algorithm appears in part a of the figure below.

The iterative procedure can be applied in reverse; that is, the temporal offset between the reference regressor and the next time series is set to be –TR. A negative lag simply means that the cross correlation will be maximized for fluctuations in the search time series that precede fluctuations in the reference time series. Thus, one may iterate forwards (positive TR lags) or backwards (negative TR lags) in time, relative to the start point. Refinement of the initial seed selection can also be made based on the results of a first pass through the data. One can even use the time series corresponding to the highest number of voxels obtained in a first pass as the optimal seed regressor for a second analysis; a form of signal averaging. The recursive approach is robust against initial seed conditions. That is, the recursive correlations tend to converge to a similar result whether one starts with mean GM signal, an SSS seed or almost any random seed. In part b of the figure below, a blue circle indicates that the number of voxels sharing fluctuations with a single voxel seed is quite small; only 200-300 voxels. A black circle indicates the set of voxels to be used in a second, optimized analysis. There is a set of 5000 voxels that have common fluctuations in the band 0.05 – 0.2 Hz.

Once a full set of regressor waveforms has been produced recursively, the entire set of regressor time courses is used in a GLM to produce a set of z maps of the voxel locations obtained at each time shift. The entire recursive procedure is shown in the figure below. Example z maps produced from the GLM appear in part c.


Fig. 2 from Tong & Frederick (2014).

 
To view the passage of the systemic flow through the brain, each z map in the set is normalized and can then be played as a movie, one frame for each TR increment assessed. In the movie below we see the z maps obtained at 2.5 frames per second (fps), i.e. TR = 0.4 sec, played back at 6.7 fps, for a changing three-plane view through the brain. The top row was produced with the optimal seed, the bottom row was produced with a local seed. As expected, the results of the recursive procedure converge to similar results regardless of the starting seed.


 (The original Supplemental Movie 1 can be downloaded here.)


The flow pattern in the movie is described by Tong & Frederick thus:
"The LFOs are “piped” into the brain though big arteries (e.g., internal carotid artery) with no phase shift. They then follow different paths (arterioles, capillaries, etc.) as branches of the cerebral vasculature diverge. It is expected that each signal would evolve independently as it travels along its own path. The observation that some of them have evolved in a similar way, and at a similar pace, is probably due to the uniformity in the fundamental structures of the cerebral blood system, likely reflecting the self-invariant properties of fractal structures found throughout biological systems."

An alternative way to view the data is as a lag map which plots the arrival time in seconds, relative to the mean arrival time assigned zero:



 
The regions fed by middle cerebral arteries appear in blue and have the earliest arrival times, while the venous drainage is colored red-yellow. Note also how symmetric the arrival times appear. For a normal, healthy brain, this is as we should expect.

At this point we can go back and revisit the issue of seed selection: fixed time shift analysis or recursive approach? Is there really a benefit to the recursive approach? Aso et al. recorded three 5-minute blocks of BOLD data under conditions of rest, a simple reaction time task (ITI of 6-24 sec), or 10 second breath holds with 90 sec normal breathing. The arrival time maps (for which they use a reversed sign convention; negative values are later arrival) for the three conditions are somewhat similar but have noticeable differences. This is the group averaged response (N=20) using the recursive time shift method:

Fig. 6D from Aso et al. (2017)

The distribution of arterial (early arriving) regions, displayed above in yellow-red, are clearly different even as the general patterns are preserved across conditions. The intra-class correlation coefficient is above 0.7. This fits with our general assumptions about BOLD data: there's a lot going on and sorting out the parts is unmaking a sausage!

The most striking result is in their comparison of the recursive procedure to a fixed SSS seed analysis. Here, they show map of the intra-class correlation coefficient for the three conditions. The recursive analysis (right column) yields ICC values significantly greater than with the SSS seed analysis (left column):

Fig. 7 from Aso et al. (2017)

The recursive procedure maintains an ability to track the hemodynamics even as there are behavioral differences imposed on the time series. The SSS seed produces more variable results, consistent with the idea that low frequency fluctuations in a large venous vessel are quite different to the spatial-temporal spread imposed by brain tissue. The recursive method, while still biased towards the venous side of the brain due to greater BOLD sensitivity, does a better job of tracking the blood dynamics upstream, into the brain tissue.


Applications of time shift analysis

Assessing the blood flow patterns in normal brain is very interesting. The extensive work that went into establishing sLFO as a major source of BOLD variability is highly relevant to the many approaches that try to account for physiological variations as sources of "noise" in resting-state fMRI data in particular. And we've seen that the recursive procedure is able to find differences between rest, a simple task and breath holding. So far so good. What else can we do with it?

To date, I have found only three studies that have used the recursive analysis: the original Tong & Frederick paper and Aso et al., both reviewed in the previous section, and a paper by Donahue et al. that I review in the next section because it uses a gas challenge rather than normal breathing. Here, I'll quickly summarize the clinical applications of the fixed seed analysis.

The earliest reference I can find to clinical application is the work of Lv et al. mentioned in the introduction. In addition to the early work from Lv et al. on stroke patients, Amemiya et al., Siegel et al., Ni et al. and Khalil et al. also assessed stroke or chronic hypoperfusion. Chen et al. used time shift analysis to look at reperfusion therapy after acute ischemic stroke. Christen et al. looked at lags in moyamoya patients, and Satow et al. looked at idiopathic normal pressure hydrocephalus. All these studies observed interesting findings in the patient groups, and many compared the time shift analysis of BOLD data to other imaging methods (e.g. MRA, DWI, DSC) for validation. I would encourage you to read the studies if you are interested in the particular pathologies. But as a representative example, I'll dig into the study by Siegel et al. because they compared the time shift analysis of BOLD data to pulsed arterial spin labeling (PASL). (See Note 2.) In regions of hypoperfusion, the regional CBF measured by pulsed ASL (PASL) was observed to decrease monotonically with the BOLD hemodynamic lag in patients at ~2 weeks after a stroke, as shown in part (b) below:

From Siegel et al. (2016).

But what changes might have persisted a year after the stroke? Would the CBF and time shift relationship be the same?
"These results raise the question of whether hypo-perfusion in the acute post-stroke period recovers in parallel with lag. To address this question, we measured change in lag (1 year minus 2 weeks) versus change in rCBF for all ROIs showing lag >0 subacutely. Although a significant relationship was present between recovery of lag, and recovery of rCBF (Pearson’s r = -0.12; P = 0.039), the variance explained by this relationship was small (r² = 0.015). This may be because overall, measures of perfusion did not change significantly between two weeks and one year post-stroke (two-week average = 85.7% of controls, one-year average = 86.4% of controls; paired t-test P = 0.3719). Thus, while a strong relationship between lag and rCBF is present sub-acutely, areas in which lag recovers do not necessarily return to normal perfusion."
The CBF remains depressed, relative to controls, but the lags resolve somewhat, as illustrated below. In this sample, four out of five patients have radically different lag maps at 1 year compared to 1-2 weeks post-stroke:

Part of Fig. 2 from Siegel et al. (2016). Lag maps for five patients at 1-2 weeks (left) and 1 year (right) after stroke.

That is very interesting. It implies that the net delivery of blood - recall that CBF has units of ml blood per 100 g tissue per minute - remains impoverished but the velocity of that blood through the ischemic region has normalized somewhat. Why might this be? If we consider CBF as a rough proxy for metabolic rate, then a simple explanation is that the metabolism of the tissue affected by the stroke is as low at 1 year as it was 2 weeks. There is probably an infarct - cells that died in the hours after the stroke - creating a persistent lower demand for glucose (and oxygen) within the broader region affected by the stroke. The vascular control mechanisms themselves, on the other hand, appear to have recovered somewhat, so the blood dynamics appear more normal even as the regional CBF remains low. (See Note 3.)

This example illustrates that time shift analysis offers different, complimentary information on a vascular disorder than is measured in PASL. Similar utility was found in the other clinical investigations where other forms of imaging, including DSC, diffusion imaging and MR angiography, were compared to the time shift analysis. There really does seem to be some unique information on offer in the time shift analysis. (See Note 4 for a bonus example, using caffeine.)


Can we increase sensitivity to blood dynamics?

The work presented so far has used standard BOLD data. Admittedly, some studies used multi-band EPI to shorten the TR, but the parameter settings were standard for a typical fMRI acquisition. That is, TE was set to generate sensitivity to T₂* changes, the flip angle was typically set to the Ernst angle, and so on. No special consideration was given to the venous bias in the acquisition. As a consequence, the data being analyzed for time lags is always likely to do better on the venous side of the brain than the arterial side, even with the more rigorous recursive time delay method. Does it have to be this way? Can we boost the sensitivity so that the recursive procedure can track arterial and venous dynamics with something approaching equal sensitivity? There are three broad approaches to ponder.

1. Change the arterial CO₂ concentration:

Rather than relying on the endogenous fluctuations of CO₂ during normal breathing, Donahue et al. used a transient hypercabia challenge to boost arterial and venous changes simultaneously. They delivered alternating 3-minute periods of medical grade air or carbogen (5% CO₂ + 95% O₂) through a mask, a procedure that has been used extensively to study cerebrovascular reactivity. The 3-minute periods during which blood gases are controlled necessitates a change in the temporal lag search window. Donahue et al. assessed lags over the range -20 to +90 seconds relative to the boxcar that describes the five 3-minute periods, using the recursive time shift method with the boxcar as the initial time series.

As we might expect for long duration events, the resulting delay maps are more homogeneous with the carbogen challenge than we've seen using endogenous BOLD fluctuations. The inherent variability of the ongoing physiology is dominated by the response to carbogen. A delay map from a normal volunteer yields almost uniform time-to-peak (TTP) for GM, and a slightly delayed TTP for some WM regions:

Fig. 2 parts (b) and (c) from Donahue et al. (2016).

But the relatively flat normal brain response makes it easy to see changes due to major disruption of the blood supply. The reduced flow through certain arteries in moyamoya patients is immediately evident as changes in TTP:

Fig. 3 parts (3) and (f) from Donahue et al. (2016).


Do we have to use long gas challenges? The 3-minute periods used by Donahue et al. are well suited to major vascular pathology such as stroke and moyamoya disease, where the transit delays can be severely abnormal and conventional measures like ASL are limited. Note the delays of 20+ seconds in the moyamoya patients compared to controls in the last two figures. That sort of disruption would be invisible to ASL methods because the label decays with T₁. If we expect the blood dynamics of interest to be more subtle, such as might arise from a pharmaceutical or a foodstuff, might shorter respiratory challenges be used in order to preserve the dynamics over a shorter range of time delays? I don't see why not. Breath holding might provide an easier alternative than the delivery of gases, too. Another consideration is the pattern of challenge used. Regularizing respiratory responses into a boxcar might not be as informative as using some amount of temporal variability. Perhaps a breathing task that samples short and long breath holds, with changes of normal breathing pace and depth, or a gas delivery paradigm that is more "stochastic." There are plenty of options to test.

2. Change the true contrast agent:

In mapping systemic LFO with BOLD we're using the paramagnetic properties of deoxyhemoglobin on the venous side, and the weak diamagnetism of arterial blood plus perhaps a small amount of inflow weighting on the arterial side. What if we moved to an exogenous contrast agent instead? For example, we might try to measure the re-circulation of a gadolinium contrast agent once the agent is assumed to have attained a steady state blood concentration. The standard approach in DSC is to map the uptake kinetics on the first pass, immediately after contrast injection. At that point, the measurement is considered complete. But it would be interesting to look at the fluctuations arising from changes in respiration rate and depth - the CO₂ sensitivity should be the same - in the minutes afterwards. The blood signal would be fully relaxed by the gadolinium, eliminating BOLD. Essentially, we would have a CBV-weighted signal. This would probably shift the bias from the venous to the arterial side. Sensitivity might take a hit as a result, but that would likely depend on the signal level surrounding arteries and capillaries. The sensitivity to CBV changes could be quite high, given the presence of gadolinium in the blood.

3. Change the pulse sequence parameters:

This is probably where most of us would start: with a standard BOLD resting state approach, no respiratory challenge or exogenous contrast agent. What options do we have in the pulse sequence parameters? Many fMRI studies use the Ernst angle for GM when establishing the flip angle (FA) at the TR being used. Can we boost the arterial signal by increasing inflow sensitivity with higher FA and/or shorter TR? (For an excellent review on inflow effects see Gao & Liu (2012).) We might use MB-EPI to attain a sub-second TR yet maintain a 90 degree excitation for maximum T₁ weighting. On the other hand, MB-EPI has a rather complex excitation pattern along the slice dimension whereas conventional EPI can be applied as either interleaved or contiguous (descending or ascending) slice ordering. Multiband forces a form of spatial interleaving so that the spin history of blood moving along the slice direction is complicated. Still, it's worth a look.

For gradient echo EPI we generally aim to set TE ~ T₂* for maximum BOLD sensitivity. For lag mapping, shorter TE may reduce the venous bias while simultaneously boosting the SNR. Spin echo EPI is another possible option. SE-EPI is used to refocus extravascular BOLD arising from large veins (check out the recent paper by Ragot & Chen for a comprehensive analysis of SE-EPI BOLD), leaving the intravascular and small vessel extravascular BOLD responses. (The BOLD signal in SE-EPI is typically about half that for GE-EPI at 3 T.) Using spin echoes also changes the T₁ recovery dynamics, something which might help add inflow sensitivity to the final signal. Now, SE-EPI does generally reduce the brain coverage per unit time, because the minimum TE is longer for SE-EPI than for GE-EPI, but multiband approaches could render the coverage acceptable. It may even be the case that 180 degree refocusing at short TR is inefficient, as well as driving up SAR, so lower excitation and refocusing FAs would be worth exploring.

Another acquisition issue given only partial consideration in time shift analysis work so far is the duration of a standard BOLD acquisition. How long should we acquire? With ASL methods, a single CBF map typically requires about 4-5 mins of data to attain reasonable SNR. Over this time we assume (usually only implicitly) that the neural activity variations are averaged so that the CBF is a reasonable reflection of the subject's baseline perfusion. For highly aroused or highly caffeinated subjects this assumption could be challenged, but whatever is true for ASL measures should apply equally well (or equally badly) to time shift analysis of BOLD data. Until someone shows us differently, then, I would suggest at least 4 minutes of data.


Conclusions

This post has looked at a method to image vascular dynamics. My intent wasn't for fMRI applications per se, even though there is a lot of overlap when the starting point is resting-state fMRI data. Rather, it's a different interpretation of resting-state data that could be informative for comparison with other blood imaging methods such as ASL. That's what I'm going to be doing with it near term. If your interests are strictly on the neuronal side, however, and you think mapping sLFO has potential for de-noising purposes, I suggest you read the sections entitled "How do systemic LFOs affect resting functional connectivity?" and "How to deal with systemic LFOs in fMRI" in my last post, and then look at the papers by Jahanian et al.,Erdogan et al., Anderson et al., and, of course, the recursive method paper by Tong & Frederick. I think the recursive approach has advantages over the fixed seed approach, as I've explained in this post. Code for the recursive lag method is available from Blaise Frederick's github. At least one person took the plunge after my last post.

I'm going to be comparing the recursive lag mapping method to pseudo-continuous ASL (PCASL) in 2019. I'll try to post regular updates as I progress.

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Notes:

1.  We have Blood Oxygenation-Level Dependent (BOLD) contrast, so shouldn't we simply define Arterial Blood Carbon Dioxide-Level Dependent contrast? That would give us ABCD-LD. Doesn't exactly trip off the tongue.

What about Arterial Blood CO₂-Level Dependent contrast, ABCO₂LD? Messy.

Or, how about ARterial CArbon DIoxide-LEvel DEpendent contrast, ARCADILEDE? Sounds better, but also sounds like a new drug for irritable bowel syndrome. ("Ask your doctor if ACADILEDE is right for you!"*Side effects may include vacating a lucrative career in industry, multiple grant disappointments, and frequent criticism from Reviewer 3.)


2.  At some point I will do an "introduction to ASL" blog post because there doesn't seem to be as widespread understanding of the method as I'd once dared to hope:


And there I was thinking you were all just being stubborn! There is sufficient evidence to suggest that a baseline CBF map, computed from a good ASL acquisition, can be a useful normalizing step for fMRI across populations when one expects systematic changes in perfusion, e.g. with aging, disease or on administration of drugs. I will be covering - eventually - this normalizing procedure in the blog post series on modulators of fMRI responses. But I'll do an intro to ASL before it, based on some work I'm doing separately with pseudo-continuous ASL (PCASL).


3.  If you're not familiar with CBF as a measure of perfusion, these last few sentences may appear contradictory. The choice of cerebral blood "flow" as the term describing the volume delivery of blood per unit time to a fixed volume of tissue - that is, perfusion - is a rather unfortunate one, since it is easily confused with the sort of laminar flow we think about for fluids in pipes. Perfusion - CBF - isn't a velocity but a rate of mass replacement. If you're confused, think about the difference of blood delivery that happens in normal GM and WM. GM has 3-5 times the metabolic demand of WM, so its CBF is around 3-5-fold higher. But the GM dynamics, as assessed by time shift analysis, aren't 3-5-fold faster. The mean transit time into WM is only a second or so longer than it is to GM. There's simply less volume replacement of blood happening in the WM tissue. How does that come about? Mostly, it's due to lower vascular density. There are fewer capillaries in the WM. The net speed of blood through GM and WM capillaries can therefore be essentially the same, but the GM perfusion is considerably higher by virtue of the greater density of capillaries.


4.  For those of you who might be interested in pharmacological manipulations, a very recent study by Yang et al. shows that time shift analysis can detect changes in blood dynamics due to caffeine ingestion. This study again utilized 90 scans available from the MyConnectome project. Yang et al. compared the 45 scans obtained on days when the subject had consumed coffee to the 45 scans conducted caffeine-free. (I leave open the possibility that Russ was simply more grumpy sans coffee and that drove the results ;-) The analysis used the same procedure as described above for the arterial to venous seed comparison (see the third figure in this post, from Tong et al. (2018)). Using seeds in superior sagittal sinus (SSS), internal carotid arteries (ICA) and the global signal (GS), Yang et al. found the transit time from ICA to SSS was almost a second longer without caffeine, comprising a delay of approximately half a second between the ICA and GS and another half a second between the GS and the SSS:

Fig. 2 from Yang et al. (2018).

The response was reasonably uniform across the brain. The results were consistent with vasoconstriction, an expected response to caffeine.

In the discussion section of the paper the authors dig into the implications of slowed blood dynamics. In particular, they try to reconcile the slower dynamics with the reduced CBF that has been reported in earlier studies on caffeine consumption. (There are no ASL data in MyConnectome to make direct comparisons so the comparisons are necessarily between studies.) There is a suggestion that mapping CBF with ASL and blood dynamics with BOLD data will greatly enhance our understanding of the neural and vascular effects under a variety of conditions. Lots of complimentary information!



Using multi-band (aka SMS) EPI on on low-dimensional array coils

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The CMRR's release notes for their MB-EPI sequence recommend using the 32-channel head coil for multiband EPI, and they caution against using the 12-channel head coil:

"The 32-channel Head coil is highly recommended for 3T. The 12-channel Head Matrix is not recommended, but it can be used for acceptable image quality at low acceleration factors."

But what does "low acceleration" mean in practice? And what if your only choice is a 12-channel coil? Following a couple of inquiries from colleagues, I decided to find out where the limits might be.

Let's start by looking at the RF coil layout, and review why the 12-channel coil is considered an inferior choice. Is it simply fewer independent channels, or something else? The figure below shows the layout of the 12-ch and 32-ch coils offered by Siemens:

From Kaza, Klose & Lotze (2011).

In most cases, the EPI slice direction will be transverse or transverse oblique (e.g. along AC-PC), meaning that we are slicing along the long axis of the magnet (magnet Z axis) and along the front-to-back dimension of the head coil. Along the long axis of the 12-ch coil there is almost no variation in the X-Y plane. At the very back of the coil the loops start to curve towards a point of convergence, but still there is no distinction in any direction in the X-Y plane. Compare that situation to the 32-ch coil. It has five distinct planes of coils along the Z axis. With the 32-ch coil, then, we can expect the hardware - the layout of the loops - to provide a good basis for separating simultaneously acquired axial slices, whereas there is no such distinct spatial information available from the coil elements in the 12-channel coil. In the 12-channel coil, every loop detects a significant and nearly equal fraction of any given slice along Z.

There is an additional complication for the Siemens 12-channel coil. It is what Siemens call a "Total Imaging Matrix (TIM)" coil. This means that, depending on a software setting, the signals from the twelve loops can be combined in ways that can lead to better receive-field heterogeneity, or higher SNR, or the whole ensemble can be left as an array coil. The maximum amount of receive field heterogeneity is produced from the "Triple" mode, so that's what I'll use here.

Modern simultaneous multi-slice (SMS) sequences use a scheme called blipped CAIPI to assist in the separation of slices at the reconstruction stage. I've not found a didactic review that can get you up to speed on this method. (If you find one, please post a link in the comments!) The original paper by Setsompop et al. is about as accessible as I've found. For now, a brief summary should suffice. The figures below may or may not help you understand what's going on without reading the full paper!

From Setsompop et al. (2012).

The essential idea is to add a small amount of phase shift along the slice dimension, using small gradient episodes that look very similar to the blips used for phase encoding in-plane. Unlike the phase encoding blips, which are set to be fully refocused - zero net phase shift - at TE, with the blipped CAIPI scheme the phase is designed to refocus every two, three or four lines of k-space. The phase shift is designed to move the image in the field-of-view (FOV) by half, one third or one quarter of the FOV, respectively. But because the blipped CAIPI gradient is active along the slice direction, slices which differ in their Z offset will accrue a differing amount of total shift. This has the effect of encoding unique spatial information in two slices that differ in Z. Importantly, we have imparted a phase shift to the slices in deterministic fashion, meaning that we can then account for that shift at the processing phase, and return the signal to its correct location in the FOV once the slice separation procedure has been performed.

What are the implications for doing MB-EPI on a 12-channel instead of a 32-channel coil? We've already seen there is considerable unique spatial information available along the Z axis from the coil geometry in the 32-channel coil. While blipped CAIPI may improve MB slice separation, it's not being relied upon to do all the work with the 32-ch coil. The hardware carries a lot of the burden. But with the 12-channel coil, the hardware offers almost no support at all. In that case, the work of separating slices is going to rely heavily on the blipped CAIPI scheme. We are fixing it in software, not hardware, as the old engineering joke puts it.


Phantom tests

Time to test it out in practice. The 32-channel coil offers our performance standard. The idea is to keep everything constant and vary only the receive coil, and compare. But what parameters to test? We can expect performance to drop off quickly as the MB factor goes up. While I have tested MB=6 with the 32-channel coil in an earlier blog post, in practice I generally don't like using greater than MB=5, to match the number of planes of independent coil loops in the axial direction. But let's not run before we can walk. Compared to no slice acceleration, a shift to MB=2 is already an impressive gain in speed on a 12-channel coil. To keep things reasonable I tested MB=2 and MB=3 first, deciding that I would only opt for larger MB factors if these tests suggested there is even more performance available. (tl;dr the limit is between 2 and 3, no further tests are forthcoming!)

Spatial resolution is the next consideration. In the absence of acceleration, we are generally limited to voxel dimensions of about 3.5 mm if we want to cover the majority of cortex in a TR of 2 seconds. Here, I decided to push to voxel dimensions of 2.5 mm, leaving the TR at 2 seconds. It's entirely permissible to take the TR reduction offered by MB without changing the voxel dimensions, of course, but I'm primarily interested in the generation and avoidance of artifacts, not the speed limit. The increased resolution in-plane makes the gradients work harder, may require partial Fourier to keep the TE reasonable, and is generally likely to trigger artifacts largely independent of the TR.

I used a spherical gel phantom (the FBIRN phantom) in the first set of comparisons. The slices were axial. An oblique axial prescription - say, AC-PC - is only likely to improve performance, since there is some unique coil information available by the time the slice direction is coronal (slices along the Y axis of the magnet). But I didn't have time to test this theory out.

Here are the tests: 
  1. MB=2, (2.5 mm)³ voxels, with Leak Block
  2. MB=2, (2.5 mm)³ voxels
  3. MB=3, (2.5 mm)³ voxels, with Leak Block
  4. MB=3, (2.5 mm)³ voxels
  5. MB=1, (2.5 mm)³ voxels, Interleaved slice order
Leak Block is the CMRR term for split-slice GRAPPA reconstruction. When Leak Block is not used, the slice separation is performed using a slice GRAPPA algorithm. See this post for more information on the differences. I acquired one run without MB acceleration (MB=1), noting that the slice order was interleaved even though I generally prefer to use contiguous slice ordering for conventional EPI (so that head motion in the slice direction doesn't cause prominent striping). An interleaved slice order is used for SMS, although the entire notion of interleaving is different for SMS than for regular multi-slice imaging.

I kept TR constant at 2000 ms throughout, and acquired 100 volumes for each test. Prescan normalization was enabled (with raw data also saved) for the 32-channel coil, but was disabled for 12ch and neck coils. See here, here and here for more information on the use of Prescan Normalization with receiver coils exhibiting pronounced receive field heterogeneity.

The 32-channel coil - our performance benchmark - produced good results consistently, as expected. I'm showing three views of the phantom data: 1. the in-plane dimension contrasted for the signal, 2. the in-plane dimension contrasted for ghosting and noise, and 3. the slice dimension reconstructed from the stack of slices. This will be the order for all comparisons to come. To keep the comparisons vaguely manageable, here I've omitted the MB=1 images from the 2x2 views. (You can find a bonus set of comparisons that includes MB=1 for the 32-channel coil in Note 1.)

32-channel coil, contrast set for visualization of signal. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
32-channel coil, contrast set for visualization of ghosts and noise. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
32-channel coil, contrast set for visualization of signal. Slice direction top-to-bottom, frequency encoding direction L-R.

As we should expect, MB=3 generates slightly more (and differently patterned) residual aliasing artifacts compared to MB=2, but these are visible only in the noise-contrasted view. The intensity is sufficiently weak that the artifacts aren't visible on the signal-contrasted views of the in-plane or the slice dimensions.

Here are the results for the 12-channel coil, with the contrast settings and 2x2 image layout as above:

12-channel coil, contrast set for visualization of signal. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
12-channel coil, contrast set for visualization of ghosts and noise. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
12-channel coil, contrast set for visualization of signal. Slice direction top-to-bottom, frequency encoding direction L-R.

If you look very carefully, you can see some artifacts overlapping the phantom in the signal-contrasted views for both the in-plane and slice dimensions for MB=3, whether using Leak Block or not. There are no such artifacts visible for the MB=2 data, however. It appears that we've found the performance threshold. Clearly, the artifact level would only increase for MB factors above 3. Is MB=3 usable? I would be inclined to use MB=2 without much reservation, but I would want to do many more tests with MB=3 before I commit. So let's take a look at the performance on a live human brain.


Brain tests

For the brain tests, I left all acquisition parameters as for the phantom data. Unlike the phantom, however, we now have considerable image contrast variations as well as the potential for movement. I didn't have time to acquire time series measurements for temporal SNR (tSNR) assessments, I'm afraid, so all I can offer is static views in which I've tried to pick the strongest examples of any artifacts I could find. It's not perfect, but it gives us a crude assessment.

The data obtained on the 32-channel coil are our standard:

32-channel coil, contrast set for visualization of signal. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
32-channel coil, contrast set for visualization of ghosts and noise. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
32-channel coil, contrast set for visualization of signal. Slice direction top-to-bottom, frequency encoding direction L-R.

The residual aliasing levels are comparable for both MB=2 and MB=3, with and without Leak Block. So now let's check the performance of the 12-channel coil:

12-channel coil, contrast set for visualization of signal. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
12-channel coil, contrast set for visualization of ghosts and noise. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
12-channel coil, contrast set for visualization of signal. Slice direction top-to-bottom, frequency encoding direction L-R.

As in the phantom, the residual aliasing is higher for MB=3 than for MB=2. But the artifact level is low and is only visible in the ghost-contrasted scan. There is no obvious banding artifact or residual aliasing overlapping signal regions. And, as on the phantom, Leak Block seems to make little difference.

Based on these initial tests, I would conclude that MB=2 is quite reasonable to use on the 12-channel coil, and MB=3 might be considered after a couple more tests, especially tSNR tests and artifact evaluations in the presence of subject motion.


MB-EPI on a neck coil

A few of us are interested in non-human imaging, e.g. using a neck coil for dog fMRI, or for scanning sea lion brains, like this:

Using the (human) neck coil to scan Cronut, a 3 year-old male California sea lion.

I reproduced the tests above to find out if the neck coil might be used for MB-EPI. You can see in the images below that the receive profile of the neck coil drops off quite quickly front and back. For humans, the usual procedure is to have the neck coil on the bed along with the 12-channel head coil, allowing a considerable boost of the receive field in one direction. But that's an experimental detail not directly related to the evaluation of MB-EPI. It is something to note if you are trying to position dog or sea lion brains in the most sensitive part of the coil.

You're familiar with the parameters and the layout of the final images by now. Here are the comparison images for MB=2 and MB=3, with and without Leak Block:

Neck coil, contrast set for visualization of signal. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
Neck coil, contrast set for visualization of ghosts and noise. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
Neck coil, contrast set for visualization of signal. Slice direction top-to-bottom, frequency encoding direction L-R.

There are clear artifacts in the MB=3 acquisitions, and Leak Block doesn't help. There are also subtle artifacts visible in-plane but not obviously in the slice direction for the MB=2 data. The artifact level is worse than for MB=2 on the 12-channel coil, but lower than that for MB=3 on the 12-channnel coil. Based on these results, I would avoid using MB=3 on the neck coil, but I would be tempted to use MB=2 if the particular application called for it.

I'm afraid I don't have live sea lion brain data to show so I'm using the next best thing - a live human. I tested only MB=2 on the grounds that the phantom data for MB=3 weren't encouraging. I may go back and test MB=3 on a human at a later date. For now, I am comparing the MB=2 performance to the single band reference (SBRef) images acquired at the start of a run. These SBRef images are acquired with a different effective TR, that is, at an effective TR of (TR x MB), so the T₁-weighted contrast is quite different. Still, these images provide a reasonable basis for evaluating SMS artifacts:

Neck coil, contrast set for visualization of signal. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
Neck coil, contrast set for visualization of ghosts and noise. Phase encoding direction top-to-bottom, frequency encoding direction L-R.
Neck coil, contrast set for visualization of signal. Slice direction top-to-bottom, frequency encoding direction L-R.


Not too bad. No obvious artifacts are visible in any of the MB data, confirming that use of MB=2 is likely permissible for the neck coil.

In the next post, I'll look at MB-EPI for diffusion imaging on the same three coils.

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Notes:

1.  Here is a bonus set of comparisons for the MB=2 tests, for the 12-channel and neck coils compared to both MB=2 and MB=1 with the 32-channel coil. The MB=2 and MB=1 data quality is quite similar for the 32-channel coil, except that the slice coverage is much reduced for MB=1.

Phase encoding direction top-to-bottom, frequency encoding direction L-R. Leak Block used for MB=2. Contrast set for visualization of signal.
Phase encoding direction top-to-bottom, frequency encoding direction L-R. Leak Block used for MB=2. Contrast set for visualization of ghosts and noise.
Slice direction top-to-bottom, frequency encoding direction L-R. Leak Block used for MB=2. Contrast set for visualization of signal.



Using multiband-EPI for diffusion imaging on low-dimensional array coils

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This is a continuation of the previous post looking at MB-EPI on a receive coil with limited spatial information provided by its geometry, such as the 12-channel TIM coil or the 4-channel neck coil on a Siemens Trio.

Simultaneous multi-slice (SMS), aka multi-band (MB), offers considerable time savings for diffusion-weighted imaging (DWI). Unlike in fMRI, where MB factors of 4 or more are quite common, in DWI few studies use MB factors greater than 3. While it may be feasible in principle to push the acquisition time even lower without generating artifacts using a large array coil like the Siemens 32-channel coil, we run into another consideration: heating. Heating isn't usually a concern for gradient echo MB-EPI used in conventional fMRI experiments. In fMRI, the excitation flip angles are generally 78° or less. But with DWI we have a double whammy. Not only do we want a large excitation flip angle to create plenty of signal, we also require a refocusing pulse that is, by convention, set at twice the flip angle of the excitation pulse. (The standard nomenclature is 90° for excitation and 180° for refocusing, but the actual angles may be lower than this in practice, for a variety of reasons I won't go into here.) Now the real kicker. The heat deposition, which we usually measure through the specific absorption rate (SAR), scales quadratically with flip angle. Thus, a single 180° refocusing pulse deposits as much heat as four 90° pulses! (See Note 1.) But wait! It gets worse! In using simultaneous multi-slice - the clue's in the name - we're not doing the equivalent of one excitation or refocusing at a time, but a factor MB of them. Some quick arithmetic to give you a feel for the issue. A diffusion scan run with 90° and 180° pulses, each using MB=3, will deposit fifteen times as much heat as a conventional EPI scan run at the same TR but with a single 90° pulse. On a 3 T scanner, it means we are quickly flirting with SAR limits when the MB factor goes beyond three. The only remedy is to extend TR, thereby undermining the entire basis for deploying SMS in the first place.

But let's not get ahead of ourselves. With a low-dimensional array such as the Siemens 12-channel TIM coil we would be delighted to get MB to work at all for diffusion imaging. The chances of flirting with the SAR limits are a distant dream.


Phantom tests for diffusion imaging

The initial tests were on the FBIRN gel phantom. I compared MB=3 and MB=2 for the 32-channel, 12-channel and neck coils using approximately the same slice coverage throughout. The TR was allowed to increase as needed in going from MB=3 to MB=2. Following CMRR's recommendations, I used the SENSE1 coil combine option throughout. I also used the Grad. rev. fat suppr. option to maximize scalp fat suppression, something that we have found is important for reducing ghosts in larger subjects (especially on the 32-channel coil, which has a pronounced receive bias around the periphery). For the diffusion weighting itself, I opted to use the scheme developed for the UK Biobank project, producing two shells at b=1000 s/mm² and b=2000 s/mm², fifty directions apiece. Four b=0 images are also included, one per twenty diffusion images. (For routine use we now actually use ten b=0 images, one every ten DW images, for a total of 111 directions.) The nominal spatial resolution is (2 mm)³. The TE is 94.8 ms, which is the minimum value attainable at the highest b value used.

There are over a hundred images we could inspect, and you would want to check all of them before you committed to a specific protocol in a real experiment because there might be some strange interaction between the eddy currents from the diffusion-weighting gradients and the MB scheme. For brevity, however, I will restrict the comparisons here to examples of the b=0, 1000 and 2000 scans. I decided to make a 2x2 comparison of a single band reference image (SBRef), a b=0 image (the b=0 scan obtained after the first twenty DW scans), and the first b=1000 and b=2000 images in the series. While only a small fraction of the entire data set, these views are sufficient to identify the residual aliasing artifacts that tell us where the acceleration limit sits.

First up, the results from the 32-channel coil, which is our performance benchmark. No artifacts are visible by eye for any of the b=0, b=1000 or b=2000 scans at either MB=2 or MB=3:

32-channel coil, MB=3. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image
32-channel coil, MB=2. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.


For the 12-channel coil, however, we can see residual aliasing in the b=0 scan for MB=3:

12-channel coil, MB=3. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.
12-channel coil, MB=2. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.

The SNR is too low to see the residual aliasing in the b=1000 and b=2000 scans at MB=3, but given the effects at b=0 we should assume they're there. However, I should note that the artifact I've shown above was the most prominent example I could find, suggesting that MB=3 on the 12-channel coil might be acceptable under some circumstances. The MB=2 data appear to be reasonably artifact-free throughout.

If you're wondering what the rendered slice dimension looks like, I'm sparing you an even lengthier post. However, I found that artifacts were more prominent in-plane than through plane. This is different to the situation with MB-EPI for fMRI, where artifacts are either similarly visible in each view, or banding may be visible in the slice dimension when there are no in-plane artifacts visible. Could it be the use of SENSE1 coil combination option, perhaps? I will try to learn more about the differences in further tests when I get the time. It's also interesting that contrasting at the noise level didn't lead to different conclusions than simply contrasting at the signal level, so again I've given just the one contrast to keep the post manageable.

Back to data. The neck coil exhibits clear residual aliasing for MB=3 at b=0 and, if you have a good eye, you can see artifacts at b=1000, too:

4-channel neck coil, MB=3. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.

I was also able to find some residual aliasing in a few of the b=0 scans at MB=2, but they tended to be at one end of the phantom. This suggests a magnetic field homogeneity effect because it's hard to shim well the flat ends of a cylinder. As always, I've shown the clearest artifact example I could find in the figure below. Most of the slices for b=0 didn't resemble a tennis ball:

4-channel neck coil, MB=2. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.

Does the presence of some artifacts in b=0 images at just MB=2 mean that multi-band is unacceptable on the neck coil? Not necessarily. It just means we'd have to be extra careful before using it for real at MB=2, and I don't think I would want to risk MB=3 on that coil. But we would want to look very carefully at regions of poor magnetic field homogeneity for artifacts in brain data. Talking of brains....


Brain tests

Time constraints didn't permit me to acquire brain data for MB=3, only for MB=2, on all three coils. I do have an earlier comparison for MB=3 and MB=2 for the 32ch and 12ch coils, however, which I'll come back to at the end. Let's first look at MB=2 on all three coils.

The acquisition parameters for brain testing are the same as for the phantom tests. Again, I compare a 2x2 matrix comprising the SBRef image, an example b=0 image, and the first b=1000 and b=2000 scans from the full DW acquisition. There will be two views apiece: the in-plane view, which is as the data are acquired, and then a rendered view of the slice dimension to see how slice leakage or banding artifacts might manifest, just in case the heterogeneity of brain introduces something new. Finally, to see how artifacts and SNR propagate through to final results, I'll compare a simple tensor analysis of the full data set. I'll show the apparent diffusion coefficient (ADC) map, a trace image, a fractional anisotropy (FA) map in grayscale, and then a color FA image. The tensor analysis option on the scanner was used to produce these processed images.

Here are the MB=2 brain results for the 32-channel coil:

32-channel coil, MB=2. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.
32-channel coil, MB=2. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.
32-channel coil, MB=2. TL: ADC image. TR: tensor trace image. BL: FA map. BR: Color FA image.


No problems in the 32-channel coil data. Nor, it turns out, for data from the 12-channel coil:

12-channel coil, MB=2. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.
12-channel coil, MB=2. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.
12-channel coil, MB=2. TL: ADC image. TR: tensor trace image. BL: FA map. BR: Color FA image.


This result is encouraging for the use of MB=2 on the 12-channel coil. At the end I'll show color FA images that suggest it might be permissible to go as far as MB=3 on the 12-channel coil, but you would definitely want to run your own phantom tests first. Then, in brains, I would pay particularly close attention to regions of high magnetic field heterogeneity - the usual suspects: frontal lobes, temporal lobes, deep brain - because of the suggestion above, in the phantom data, of a shim-related residual aliasing for MB=3.

How did the neck coil do?

4-channel neck coil, MB=2. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.
4-channel neck coil, MB=2. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image.
4-channel neck coil, MB=2. TL: ADC image. TR: tensor trace image. BL: FA map. BR: Color FA image.


Overall, not too bad. There are no artifacts visible to the naked eye, which is encouraging for those of us who might want to (or be forced to) use the neck coil for non-human brains. But there is a clear degradation of signal-to-noise overall, compared to the other two coils. This three-way comparison of the color FA maps shows it pretty well:



Although the slices don't match exactly (sorry!), it's still possible to discern the noisier data produced in going from the 32-channel to the 12-channel coil, and from the 12-channel to the neck coil. There is a more mottled - less smooth - appearance as you move left to right. It's not a surprise to see SNR degrade in the order shown. Not only does the number of receive channels decrease, but the "filling factor" - the amount of coil filled with brain versus space - also decreases from 32ch to 12ch to neck coil. Still, there are no discrete artifacts, suggesting that MB=2 is acceptable on the 12-channel coil. Likewise, the neck coil produces reasonable-looking results on a real brain in spite of the subtle residual aliasing artifacts we saw in the phantom data. If the lower SNR was a problem, a simple tactic would be to increase the voxel size from (2 mm)³ to, say, (2.2 mm)³ for a 33% SNR boost.

Is the SNR worse for MB=2 than it would be for un-accelerated DWI? That's a test I didn't do, but will. It would be an interesting comparison, because the total acquisition time would be above 12 minutes without MB, rendering the entire experiment more susceptible to motion. It is entirely possible that the SNR would end up lower without MB! Except that an earlier test I ran, comparing MB=2 and MB=3 on the 12-channel and 32-channel coils only, suggests that MB does indeed reduce the SNR, even as it shortens the total acquisition time:





In sum, then, I think there is considerable scope to use MB for diffusion imaging on coils with limited spatial information or number of channels. The limits for MB factor appear to be quite similar for diffusion imaging as I found for fMRI applications in the last post.

__________________________


Notes:

1.  SAR also scales quadratically with B₀, so don't assume that anything you can do at 3 T will be approximately twice as demanding if run at 7 T. The actual demands will be (7x7)/(3x3) = 5.4 times greater! You might be able to use your 7 T to reheat your coffee between subject scans!




Restraining the 32-channel coil

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There has been a move towards custom head restraint in recent years. These devices are tailored to fit the subject in such a way that any movement of the head can be transmitted to the coil. It is therefore imperative to make sure that the RF coil is also well restrained.

On Siemens Trio and Prisma scanners, the 32-channel head coil is a special case. It was designed independent of the standard head coils. Restraint on the bed is thus a bit of an afterthought. Sticky pads on the base of the coil are designed to prevent movement through friction, but there are gaps on all four sides and no specific mechanism - slots, grooves, etc. - to lock the coil into a particular position. On my Trio, I was in the habit of putting the 32-channel coil all the way back to the frame of the bed, assuming that the most likely direction of motion from a subject would be backwards. Problem solved, right? No. By putting the coil all the way back, when using custom head restraint I actually put stress on the front two coil cables and this led to intermittent receive RF artifacts. A more refined fix was necessary.

My engineer built a simple frame (see photos below) that fits snugly into the rear portion of the bed frame and forces the coil onto protrusions that hold the standard (12-channel) coils properly. It also shims out the left and right gaps so there is no chance of side to side motion, either. With this device in place, the coil can only go one way: up. 

There has been some debate in the literature about the utility of custom head restraint for motion mitigation, with one group finding benefits while another found it made things worse. I note that both groups were using 32-channel coils on a Prisma, so proper head coil restraint may be a reason for different outcomes. I am now working on a fix for Prisma scanners and will do a separate post on the solution once it's been tested. (ETA April-May.) Until then, if you use a 32-channel coil on any Siemens scanner, my advice is to use additional restraint and make sure your coil is in a reliable, stable position. 

 

The coil restraint shim is put into position before the 32-channel coil.


Coil restraint shim in position.






A core curriculum for fMRI?

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Blimey. Judging by the reaction to my earlier Tweet, there's something to be done here. And it makes sense because fMRI has been around for thirty years yet seems to be as ad hoc today as it was at its genesis. We're half the age of modern electronic computing, twice as old as Facebook and Twitter. FMRI predates the NCSA Mosaic web browser, for goodness sake. Let that sink in for a minute.

This is something I've been pondering for a long time. In 2010 I thought I might write a textbook to capture what I saw as the fundamental knowledge that every fMRIer would need to know to set up and run an experiment. I started writing this blog as a way to draft chapters for the textbook. The textbook idea got, uh, shelved as early as 2011, once I realized that a blog is better-suited to delivering content on a subject that is inherently dynamic. Try embedding a movie in a textbook! But then the blog, in its original guise, sorta ran out of steam a few years ago, too. And the main reason why I ran out of steam is directly relevant to this post. I was getting into areas about which I know little to nothing, in an attempt to be able to write blog posts relevant to fMRI research. Take the post series on "fMRI data modulators," my rather clunky term for "that which causes your fMRI time series to vary in ways you probably don't want." I was having to try to teach myself respiratory and vascular physiology from scratch. The last time I sat in a formal biology class I was 13. Recently, I've encountered machine learning, glucose metabolism, vascular anatomy and a slew of other areas about which I know almost nothing. Where does one start????

On the assumption that I'm not alone, it would seem there's a trade to be made. If I can teach k-space to a psychologist, surely a statistician can teach an anatomist about normal distributions, a biochemist can teach an electrical engineer about the TCA cycle, and so on. With very few exceptions, all of us could really use better foundational knowledge somewhere. We are all impostors!

No doubt your first reaction is "Sounds lovely, but nobody has the time!" I respectfully disagree. You are likely already spending the time. My suggestion is to determine whether there might be a more efficient way for you to spend your time, by joining a pool of like-minded "teachers" who will cover the things you can't or won't cover. So, here is a throwaway list of things to consider before you pass judgment:

  • We are all trying to do/learn/teach the same things! There ought to be a more efficient way to do it.
  • The core concepts needed to understand and run fMRI experiments change relatively slowly. The shelf life of the fundamentals should last a decade or more. Updates can be infrequent.
  • Most of us have limited teaching resources. Few, if any institutions can cover all the core areas well.
  • My students become your postdocs. Wouldn’t you want them to arrive with a solid base?
  • Today’s students are tomorrow’s professors. If we are to improve teaching overall, we have to start at the bottom, not at the top.
  • A lot of topical problems (including poor replication, double-dipping, motion sensitivity, physiologic nuisance fluctuations) could be reduced at source by people setting up and executing better experiments through deeper knowledge. Crap in, crap out.
  • We are all super busy, yet the effort to contribute to a distributed syllabus could be a wash, perhaps even a net reduction, because you won't have to BS your way through stuff you don't really understand yourself.
  • I want to learn, too! It’s hard to determine an efficient path through new areas! I need a guide.

 

That just leaves the final step: doing it. Until he regrets his offer, Pradeep Raamana has generously offered use of his Quality Conversations forum to commence organizing efforts. I envision a first meeting at which we attempt to define all the main areas that comprise a "core syllabus" for fMRI. This would include, at the very least, NMR physics, MRI physics, various flavors of physiology, some biochemistry, neuroanatomy, basic statistics, machine learning, experimental design and models, scanner design, etc. If we can identify 6-8 umbrella areas then I'd look to create teams for each who would actually determine what they consider to be core, or fundamental, to their domain. Most likely, it's the stuff with a very long shelf life. We're not trying to be topical, the goal is to give everyone practicing fMRI a basic common framework. We want to define the equivalents of the Periodic Table in chemistry, Newtonian mechanics in physics, eukaryotic cell structure in biology, etc.

Doable? Drop your thoughts below.


Core curriculum: An introduction

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After much delay, I am finally going to start developing the core curriculum I suggested in December 2021. At that time, I imagined recruiting a group of 10-15 domain experts to provide the bulk of material under each separate discipline. That might have worked. Indeed, it could still work if an appropriate group such as the OHBM education committee decides to have a go. But I'm going to try something different. To borrow a phrase from blockchain folks, I want to be permissionless. I'm going to try to collate publicly available material myself, with occasional assistance from others if and when I get proper stuck. Trying to do it all myself should provide me with an interesting set of learning experiences, I hope, and it should also help guarantee that anyone, anywhere with access to YouTube can participate.

So, how's this gonna go? Not sure, it's an experiment. I have the following main disciplines listed and as of now I plan on tackling them in this order (although I may well start on some of the later ones before finishing the earlier ones). I'm just gonna start and see what happens. I will aim for one post a week, equivalent to 1-2 hours of learning. As I go, I will do my best to organize the collection - for example, all will have Core curriculum somewhere in the title, plus appropriate labels - and once there are enough of them I'll create a main page with links; a virtual contents table.

Likely major themes, in likely order:

  • How to learn from videos
  • Mathematics
  • Physics
  • Engineering
  • Biology
  • Biophysics
  • Image processing & analysis
  • Statistics
  • Psychology
  • Experimental design
  • Practical issues

Why this order? The logic is to try to build concepts on concepts. It's hard to understand most important engineering concepts without a decent understanding of some physics, which itself requires some decent understanding of certain mathematics, and so on. And, as noted in my Dec 2021 post, the goal here is to cover material that is non-volatile over decades. It's about the fundamental concepts, not the state-of-the-art. 

Right, enough preamble. Time to get going! 

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Infrequently asked questions:

Q: Where's your Twitter?  A: Gawn, all gawn. Got X'd out.

Q: Can we comment or make suggestions?  A: Yup. I'll do my best to answer comments to the posts, and my email still works.

Q: What do you mean by "non-volatile over decades?"  A: I'm taking my inspiration from the established sciences. Consider chemistry. Any chemist trained in a university anywhere in the world understands the Periodic Table and why the first row transition elements are different from the noble gases. They also understand carbon valence, pH, catalysis and hopefully some thermodynamics. These subjects are all fundamental to the field of chemistry and are unchanged whether they are learned in England, Sri Lanka or Venezuela. They also haven't changed fundamentally since I learned about them in the 1980s. 

Q: Why Blogger and not Substack or some newer platform?  A: Inertia. There's a dozen years of history on this site and a lot of it still applies. Indeed, I hope some of it will be getting re-used in the core curriculum! 

Q: Are you going to go back to more topical tips?  A: I don't have plans to, but if there's something important to cover then I may. However, I won't be going back to writing the series on fMRI artifacts or physiological confounds, at least not at this time. I'm focused on the fundamentals right now. Seeing way too many un(der)prepared folk still coming into neuroimaging.


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